sum_of_squares se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
29 questions tagged with sum_of_squares.
B. (11)
छोटी संख्या (x) हो तो बड़ी (x+9) है। (x-2+(x+9)2=481) से (x=11) मिलता है। / Let the smaller number be (x), so the larger is (x+9). From (x-2+(x+9)2=481), (x=11).
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The sum of the squares of two consecutive positive odd numbers is (394). What is the smaller number?
B. (13)
संख्याएँ (x) और (x+2) हों तो (x-2+(x+2)2=394)। इससे (x=13) है। / If the numbers are (x) and (x+2), then (x-2+(x+2)2=394). This gives (x=13).
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C. (12)
छोटी संख्या (x) हो तो (x-2+(x+9)2=585)। इससे (x=12) मिलता है। / If the smaller number is (x), then (x-2+(x+9)2=585). This gives (x=12).
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The sum of the squares of two consecutive natural numbers is (365). Which numbers are they?
C. (13) और (14)(13) and (14)
संख्याएँ (x) और (x+1) लें। (x-2+(x+1)2=365) से (x=13) मिलता है। / Take the numbers as (x) and (x+1). From (x-2+(x+1)2=365), we get (x=13).
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B. (42)
संख्याएँ (x) और (90-x) मानें। (x-2+(90-x)2=4068) से संख्याएँ (42) और (48) मिलती हैं। / Take the numbers as (x) and (90-x). From (x-2+(90-x)2=4068), the numbers are (42) and (48).
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The sum of squares of two consecutive even positive numbers is (3044). What is the larger number?
C. (40)
लगातार सम संख्याएँ (x) और (x+2) हैं। (x-2+(x+2)2=3044) से (x=38), इसलिए बड़ी संख्या (40) है। / Consecutive even numbers are (x) and (x+2). From (x-2+(x+2)2=3044), (x=38), so the larger number is (40).
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The sum of squares of two consecutive odd positive numbers is (2314). What is the smaller number?
C. (33)
लगातार विषम संख्याएँ (x) और (x+2) होंगी। (x-2+(x+2)2=2314) से (x=33) है। / Consecutive odd numbers are (x) and (x+2). From (x-2+(x+2)2=2314), (x=33).
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The sum of squares of two consecutive positive integers is (1513). What is the smaller integer?
C. (27)
छोटा पूर्णांक (x) हो तो (x-2+(x+1)2=1513), जिससे (x=27) मिलता है। लगातार पूर्णांकों को (x) और (x+1) लिखें। / If the smaller integer is (x), then (x-2+(x+1)2=1513), giving (x=27). Write consecutive integers as (x) and (x+1).
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B. (36)
संख्याएँ (x) और (80-x) मानें। (x-2+(80-x)2=3232) से संख्याएँ (36) और (44) मिलती हैं। / Take the numbers as (x) and (80-x). From (x-2+(80-x)2=3232), the numbers are (36) and (44).
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The sum of squares of two consecutive even positive numbers is (2452). What is the larger number?
C. (36)
लगातार सम संख्याएँ (x) और (x+2) हैं। (x-2+(x+2)2=2452) से (x=34), इसलिए बड़ी संख्या (36) है। / Consecutive even numbers are (x) and (x+2). From (x-2+(x+2)2=2452), (x=34), so the larger number is (36).
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The sum of squares of two consecutive odd positive numbers is (2050). What is the smaller number?
C. (31)
लगातार विषम संख्याएँ (x) और (x+2) होंगी। (x-2+(x+2)2=2050) से (x=31) है। / Consecutive odd numbers are (x) and (x+2). From (x-2+(x+2)2=2050), (x=31).
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The sum of squares of two consecutive positive integers is (1201). What is the smaller integer?
C. (24)
छोटा पूर्णांक (x) हो तो (x-2+(x+1)2=1201), जिससे (x=24) मिलता है। लगातार पूर्णांकों को (x) और (x+1) लिखें। / If the smaller integer is (x), then (x-2+(x+1)2=1201), giving (x=24). Write consecutive integers as (x) and (x+1).
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B. (30)
संख्याएँ (x) और (65-x) हों तो (x-2+(65-x)2=2125) बनता है। हल से संख्याएँ (30) और (35) मिलती हैं। / If the numbers are (x) and (65-x), then (x-2+(65-x)2=2125). Solving gives (30) and (35).
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The sum of squares of two consecutive even positive numbers is (1924). What is the larger number?
C. (32)
लगातार सम संख्याएँ (x) और (x+2) मानें। (x-2+(x+2)2=1924) से (x=30), इसलिए बड़ी संख्या (32) है। / Let the consecutive even numbers be (x) and (x+2). From (x-2+(x+2)2=1924), (x=30), so the larger number is (32).
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The sum of squares of two consecutive odd positive numbers is (1570). What is the smaller number?
C. (27)
लगातार विषम संख्याएँ (x) और (x+2) हैं। (x-2+(x+2)2=1570) से (x=27) मिलता है। / Consecutive odd numbers are (x) and (x+2). From (x-2+(x+2)2=1570), (x=27).
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The sum of squares of two consecutive positive integers is (841). What is the smaller integer?
C. (20)
छोटा पूर्णांक (x) हो तो (x-2+(x+1)2=841), जिससे (x=20) मिलता है। लगातार संख्याओं को (x) और (x+1) लिखें। / If the smaller integer is (x), then (x-2+(x+1)2=841), giving (x=20). Write consecutive numbers as (x) and (x+1).
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The sum of two numbers is (26) and the sum of their squares is (340). What is the larger number?
A. (14)
यदि एक संख्या (x) है, तो दूसरी (26-x) होगी। (x-2+(26-x)2=340) से संख्याएँ (14) और (12) हैं। / If one number is (x), the other is (26-x). From (x-2+(26-x)2=340), the numbers are (14) and (12).
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A. (13)
यदि छोटी संख्या (x) है, तो बड़ी (x+4) है। (x-2+(x+4)2=250) से (x=9), इसलिए बड़ी संख्या (13) है। / If the smaller number is (x), the larger is (x+4). From (x-2+(x+4)2=250), (x=9), so the larger number is (13).
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C. (25)
संख्याएँ (x) और (55-x) हों, तब (x-2+(55-x)2=1525) बनता है। हल से संख्याएँ (25) और (30) मिलती हैं। / Let the numbers be (x) and (55-x), then (x-2+(55-x)2=1525). Solving gives (25) and (30).
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The sum of squares of two consecutive even positive numbers is (1060). What is the larger number?
C. (24)
लगातार सम संख्याएँ (x) और (x+2) मानें। (x-2+(x+2)2=1060) से (x=22), इसलिए बड़ी संख्या (24) है। / Let the consecutive even numbers be (x) and (x+2). From (x-2+(x+2)2=1060), (x=22), so the larger number is (24).
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The sum of squares of two consecutive odd positive numbers is (650). What is the smaller number?
B. (17)
लगातार विषम संख्याएँ (x) और (x+2) हैं। (x-2+(x+2)2=650) से (x=17) मिलता है। / Consecutive odd numbers are (x) and (x+2). From (x-2+(x+2)2=650), (x=17).
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The sum of squares of two consecutive positive integers is (365). What is the smaller integer?
C. (13)
छोटा पूर्णांक (x) हो तो (x-2+(x+1)2=365), जिससे (x=13) मिलता है। लगातार पूर्णांकों को (x) और (x+1) लिखें। / If the smaller integer is (x), then (x-2+(x+1)2=365), giving (x=13). Write consecutive integers as (x) and (x+1).
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The sum of two numbers is (22) and the sum of their squares is (250). What is the larger number?
A. (15)
यदि एक संख्या (x) है, तो दूसरी (22-x) होगी। (x-2+(22-x)2=250) से संख्याएँ (15) और (7) हैं। / If one number is (x), the other is (22-x). From (x-2+(22-x)2=250), the numbers are (15) and (7).
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A. (9)
यदि छोटी संख्या (x) है, तो बड़ी (x+2) है। (x-2+(x+2)2=130) से (x=7), इसलिए बड़ी संख्या (9) है। / If the smaller number is (x), the larger is (x+2). From (x-2+(x+2)2=130), (x=7), so the larger number is (9).
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If \(\alpha\) and \(\beta\) are roots of \(x^2-6x+2=0\), what is the value of \(\alpha^2+\beta^2\)?
A. (32)
यहां \(\alpha+\beta=6\) और \(\alpha\beta=2\) है। \(\alpha^2+\beta^2=36-4=32\) है। / Here \(\alpha+\beta=6\) and \(\alpha\beta=2\). \(\alpha^2+\beta^2=36-4=32\).
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If \(\alpha\) and \(\beta\) are roots of \(x^2-4x+1=0\), what is the value of \(\alpha^2+\beta^2\)?
A. (14)
यहां \(\alpha+\beta=4\) और \(\alpha\beta=1\) है। \(\alpha^2+\beta^2=16-2=14\) है। / Here \(\alpha+\beta=4\) and \(\alpha\beta=1\). \(\alpha^2+\beta^2=16-2=14\).
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What is the sum of squares of the roots of \(x^2-9x+14=0\)?
A. (53)
यहां \(\alpha+\beta=9\) और \(\alpha\beta=14\) है। \(\alpha^2+\beta^2=81-28=53\) होगा। / Here \(\alpha+\beta=9\) and \(\alpha\beta=14\). Thus \(\alpha^2+\beta^2=81-28=53\).
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What is the sum of squares of the roots of \(x^2-7x+10=0\)?
A. (29)
यहां \(\alpha+\beta=7\) और \(\alpha\beta=10\) है। \(\alpha^2+\beta^2=49-20=29\) होगा। / Here \(\alpha+\beta=7\) and \(\alpha\beta=10\). Thus \(\alpha^2+\beta^2=49-20=29\).
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What is the sum of squares of the roots of \(x^2-6x+5=0\)?
A. (26)
यहां \(\alpha+\beta=6\) और \(\alpha\beta=5\) है। \(\alpha^2+\beta^2=36-10=26\) होगा। / Here \(\alpha+\beta=6\) and \(\alpha\beta=5\). Thus \(\alpha^2+\beta^2=36-10=26\).
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