Question 1/3
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि \(x^2-5x+1=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\alpha^4+\beta^4\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-5x+1=0\), what is \(\alpha^4+\beta^4\)?
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=5\) and \(\alpha\beta=1\). First \(\alpha^2+\beta^2=23\), then \(\alpha^4+\beta^4=23^2-2=527\).
Step 2
Why this answer is correct
The correct answer is A. (527). Here \(\alpha+\beta=5\) and \(\alpha\beta=1\). First \(\alpha^2+\beta^2=23\), then \(\alpha^4+\beta^4=23^2-2=527\).
Step 3
Exam Tip
\(\alpha+\beta=5\) और \(\alpha\beta=1\) है। पहले \(\alpha^2+\beta^2=23\), फिर \(\alpha^4+\beta^4=23^2-2=527\)।
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Question 2/3
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि \(x^2-3x+1=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\alpha^4+\beta^4\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-3x+1=0\), what is \(\alpha^4+\beta^4\)?
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=3\) and \(\alpha\beta=1\). First \(\alpha^2+\beta^2=7\), then \(\alpha^4+\beta^4=7^2-2=47\).
Step 2
Why this answer is correct
The correct answer is C. (47). Here \(\alpha+\beta=3\) and \(\alpha\beta=1\). First \(\alpha^2+\beta^2=7\), then \(\alpha^4+\beta^4=7^2-2=47\).
Step 3
Exam Tip
\(\alpha+\beta=3\) और \(\alpha\beta=1\) है। पहले \(\alpha^2+\beta^2=7\), फिर \(\alpha^4+\beta^4=7^2-2=47\)।
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Question 3/3
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि \(x^2-4x+1=0\) की जड़ें \(\alpha,\beta\) हैं, तो \(\alpha^4+\beta^4\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-4x+1=0\), what is \(\alpha^4+\beta^4\)?
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=4\) and \(\alpha\beta=1\). First \(\alpha^2+\beta^2=14\), then \(\alpha^4+\beta^4=14^2-2=194\).
Step 2
Why this answer is correct
The correct answer is A. (194). Here \(\alpha+\beta=4\) and \(\alpha\beta=1\). First \(\alpha^2+\beta^2=14\), then \(\alpha^4+\beta^4=14^2-2=194\).
Step 3
Exam Tip
\(\alpha+\beta=4\) और \(\alpha\beta=1\) है। पहले \(\alpha^2+\beta^2=14\), फिर \(\alpha^4+\beta^4=14^2-2=194\)।
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