Here \(\alpha+\beta=7\) and \(\alpha\beta=10\). Since \(\alpha^2+\beta^2=49-20=29\), the value is (29-6(7)=-13), so none of the options is correct.
Step 2
Why this answer is correct
The correct answer is B. (-11). Here \(\alpha+\beta=7\) and \(\alpha\beta=10\). Since \(\alpha^2+\beta^2=49-20=29\), the value is (29-6(7)=-13), so none of the options is correct.
Step 3
Exam Tip
\(\alpha+\beta=7\) और \(\alpha\beta=10\) है। \(\alpha^2+\beta^2=49-20=29\), इसलिए (29-6(7)=-13), अतः विकल्पों में कोई सही नहीं है।
We use (\(\alpha-5\)\(\beta-5\)=\alpha\beta-5\(\alpha+\beta\)+25). Since \(\alpha+\beta=4\) and \(\alpha\beta=-12\), the value is (-7).
Step 2
Why this answer is correct
The correct answer is A. (-7). We use (\(\alpha-5\)\(\beta-5\)=\alpha\beta-5\(\alpha+\beta\)+25). Since \(\alpha+\beta=4\) and \(\alpha\beta=-12\), the value is (-7).
Step 3
Exam Tip
(\(\alpha-5\)\(\beta-5\)=\alpha\beta-5\(\alpha+\beta\)+25) है। \(\alpha+\beta=4\) और \(\alpha\beta=-12\), इसलिए मान (-7) है।
Here \(\alpha+\beta=3\) and \(\alpha\beta=\frac{5}{4}\). Thus \(\alpha^3+\beta^3=27-\frac{45}{4}=\frac{63}{4}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{63}{4}\). Here \(\alpha+\beta=3\) and \(\alpha\beta=\frac{5}{4}\). Thus \(\alpha^3+\beta^3=27-\frac{45}{4}=\frac{63}{4}\).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=3\) और \(\alpha\beta=\frac{5}{4}\) है। \(\alpha^3+\beta^3=27-\frac{45}{4}=\frac{63}{4}\)।
Here \(\alpha^2+\beta^2=64-4=60\) and (\(\alpha\beta\)2=4). Thus \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}=\frac{60}{4}=15\).
Step 2
Why this answer is correct
The correct answer is A. (15). Here \(\alpha^2+\beta^2=64-4=60\) and (\(\alpha\beta\)2=4). Thus \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}=\frac{60}{4}=15\).
Step 3
Exam Tip
\(\alpha^2+\beta^2=64-4=60\) और (\(\alpha\beta\)2=4) है। इसलिए \(\frac{1}{\alpha^2}+\frac{1}{\beta^2}=\frac{60}{4}=15\)।
We use (\(\alpha-4\)\(\beta-4\)=\alpha\beta-4\(\alpha+\beta\)+16). Since \(\alpha+\beta=3\) and \(\alpha\beta=-10\), the value is (-6).
Step 2
Why this answer is correct
The correct answer is C. (-6). We use (\(\alpha-4\)\(\beta-4\)=\alpha\beta-4\(\alpha+\beta\)+16). Since \(\alpha+\beta=3\) and \(\alpha\beta=-10\), the value is (-6).
Step 3
Exam Tip
(\(\alpha-4\)\(\beta-4\)=\alpha\beta-4\(\alpha+\beta\)+16) है। \(\alpha+\beta=3\) और \(\alpha\beta=-10\), इसलिए मान (-6) है।
Here \(\alpha+\beta=\frac{8}{3}\) and \(\alpha\beta=\frac{4}{3}\). Using (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)), we get \(\frac{224}{27}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{224}{27}\). Here \(\alpha+\beta=\frac{8}{3}\) and \(\alpha\beta=\frac{4}{3}\). Using (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)), we get \(\frac{224}{27}\).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=\frac{8}{3}\) और \(\alpha\beta=\frac{4}{3}\) है। (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)) से \(\frac{224}{27}\) मिलता है।
We use (\frac{1}{\alpha-2}+\frac{1}{\beta-2}=\frac{\alpha-2+\beta-2}{\(\alpha\beta\)2}). Since \(\alpha^2+\beta^2=30\) and (\(\alpha\beta\)2=9), the value is \(\frac{10}{3}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{10}{3}\). We use (\frac{1}{\alpha-2}+\frac{1}{\beta-2}=\frac{\alpha-2+\beta-2}{\(\alpha\beta\)2}). Since \(\alpha^2+\beta^2=30\) and (\(\alpha\beta\)2=9), the value is \(\frac{10}{3}\).
Step 3
Exam Tip
(\frac{1}{\alpha-2}+\frac{1}{\beta-2}=\frac{\alpha-2+\beta-2}{\(\alpha\beta\)2}) होता है। \(\alpha^2+\beta^2=30\) और (\(\alpha\beta\)2=9), इसलिए मान \(\frac{10}{3}\) है।
Here \(\alpha+\beta=5\) and \(\alpha\beta=6\). Since \(\alpha^2+\beta^2=13\), the value is (13-4\(\alpha+\beta\)=13-20=-7).
Step 2
Why this answer is correct
The correct answer is A. (-7). Here \(\alpha+\beta=5\) and \(\alpha\beta=6\). Since \(\alpha^2+\beta^2=13\), the value is (13-4\(\alpha+\beta\)=13-20=-7).
Step 3
Exam Tip
\(\alpha+\beta=5\) और \(\alpha\beta=6\) है। \(\alpha^2+\beta^2=13\), इसलिए (13-4\(\alpha+\beta\)=13-20=-7)।
We use (\(\alpha+3\)\(\beta+3\)=\alpha\beta+3\(\alpha+\beta\)+9). Since \(\alpha+\beta=2\) and \(\alpha\beta=-8\), the value is (7).
Step 2
Why this answer is correct
The correct answer is A. (7). We use (\(\alpha+3\)\(\beta+3\)=\alpha\beta+3\(\alpha+\beta\)+9). Since \(\alpha+\beta=2\) and \(\alpha\beta=-8\), the value is (7).
Step 3
Exam Tip
(\(\alpha+3\)\(\beta+3\)=\alpha\beta+3\(\alpha+\beta\)+9) है। \(\alpha+\beta=2\) और \(\alpha\beta=-8\), इसलिए मान (7) है।
Here \(\alpha+\beta=\frac{5}{2}\) and \(\alpha\beta=\frac{3}{2}\). Using (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)), we get \(\frac{35}{8}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{35}{8}\). Here \(\alpha+\beta=\frac{5}{2}\) and \(\alpha\beta=\frac{3}{2}\). Using (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)), we get \(\frac{35}{8}\).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=\frac{5}{2}\) और \(\alpha\beta=\frac{3}{2}\) है। (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)) से \(\frac{35}{8}\) मिलता है।
The roots are (3) and (5). Substitution gives \(\frac{5}{1}+\frac{7}{3}=\frac{22}{3}\), so none of the options is correct; the correct value should be \(\frac{22}{3}\).
Step 2
Why this answer is correct
The correct answer is A. (8). The roots are (3) and (5). Substitution gives \(\frac{5}{1}+\frac{7}{3}=\frac{22}{3}\), so none of the options is correct; the correct value should be \(\frac{22}{3}\).
Step 3
Exam Tip
जड़ें (3) और (5) हैं। सीधे रखने पर \(\frac{5}{1}+\frac{7}{3}=\frac{22}{3}\) आता है, इसलिए विकल्पों में कोई सही नहीं; सही प्रश्न के लिए उत्तर \(\frac{22}{3}\) होना चाहिए।
We use (\frac{1}{\alpha-2}+\frac{1}{\beta-2}=\frac{\alpha-2+\beta-2}{\(\alpha\beta\)2}). Since \(\alpha^2+\beta^2=21\) and (\(\alpha\beta\)2=4), the value is \(\frac{21}{4}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{21}{4}\). We use (\frac{1}{\alpha-2}+\frac{1}{\beta-2}=\frac{\alpha-2+\beta-2}{\(\alpha\beta\)2}). Since \(\alpha^2+\beta^2=21\) and (\(\alpha\beta\)2=4), the value is \(\frac{21}{4}\).
Step 3
Exam Tip
(\frac{1}{\alpha-2}+\frac{1}{\beta-2}=\frac{\alpha-2+\beta-2}{\(\alpha\beta\)2}) होता है। \(\alpha^2+\beta^2=21\) और (\(\alpha\beta\)2=4), इसलिए मान \(\frac{21}{4}\) है।
(\(\alpha-2\)\(\beta-2\)=\alpha\beta-2\(\alpha+\beta\)+4). Since \(\alpha+\beta=6\) and \(\alpha\beta=8\), the value is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\alpha-2\)\(\beta-2\)=\alpha\beta-2\(\alpha+\beta\)+4). Since \(\alpha+\beta=6\) and \(\alpha\beta=8\), the value is (0).
Step 3
Exam Tip
(\(\alpha-2\)\(\beta-2\)=\alpha\beta-2\(\alpha+\beta\)+4) है। \(\alpha+\beta=6\) और \(\alpha\beta=8\), इसलिए मान (0) है।
(\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4). Since \(\alpha+\beta=4\) and \(\alpha\beta=2\), the value is (14).
Step 2
Why this answer is correct
The correct answer is C. (14). (\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4). Since \(\alpha+\beta=4\) and \(\alpha\beta=2\), the value is (14).
Step 3
Exam Tip
(\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4) है। \(\alpha+\beta=4\) और \(\alpha\beta=2\), इसलिए मान (14) है।
(\alpha-2\beta+\alpha\beta-2=\alpha\beta\(\alpha+\beta\)). Since \(\alpha\beta=-\frac{5}{2}\) and \(\alpha+\beta=-\frac{3}{2}\), the value is \(\frac{15}{4}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{15}{4}\). (\alpha-2\beta+\alpha\beta-2=\alpha\beta\(\alpha+\beta\)). Since \(\alpha\beta=-\frac{5}{2}\) and \(\alpha+\beta=-\frac{3}{2}\), the value is \(\frac{15}{4}\).
Step 3
Exam Tip
(\alpha-2\beta+\alpha\beta-2=\alpha\beta\(\alpha+\beta\)) होता है। \(\alpha\beta=-\frac{5}{2}\) और \(\alpha+\beta=-\frac{3}{2}\), इसलिए मान \(\frac{15}{4}\) है।
\(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\). With \(\alpha+\beta=-4\) and \(\alpha\beta=1\), the value is (14).
Step 2
Why this answer is correct
The correct answer is C. (14). \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\). With \(\alpha+\beta=-4\) and \(\alpha\beta=1\), the value is (14).
Step 3
Exam Tip
\(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\) होता है। \(\alpha+\beta=-4\) और \(\alpha\beta=1\) से मान (14) आता है।
Use (\(\alpha-\beta\)2=\(\alpha+\beta\)2-4\alpha\beta). Here \(\alpha+\beta=\frac{7}{2}\) and \(\alpha\beta=\frac{3}{2}\), so the value is \(\frac{25}{4}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{25}{4}\). Use (\(\alpha-\beta\)2=\(\alpha+\beta\)2-4\alpha\beta). Here \(\alpha+\beta=\frac{7}{2}\) and \(\alpha\beta=\frac{3}{2}\), so the value is \(\frac{25}{4}\).
Step 3
Exam Tip
(\(\alpha-\beta\)2=\(\alpha+\beta\)2-4\alpha\beta) का प्रयोग करें। यहाँ \(\alpha+\beta=\frac{7}{2}\) और \(\alpha\beta=\frac{3}{2}\), इसलिए मान \(\frac{25}{4}\) है।
