If a2 + b2 = 5ab, then the value of $$\left( {\frac{{{a^2}}}{{{b^2}}}{\text{ + }}\frac{{{b^2}}}{{{a^2}}}} \right)$$ is?
A. 32
B. 16
C. 23
D. -23
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {a^2} + {b^2} = 5ab \cr & \Rightarrow \frac{{{a^2}}}{{ab}} + \frac{{{b^2}}}{{ab}} = 5 \cr & \Rightarrow \frac{a}{b}{\text{ + }}\frac{b}{a}{\text{ = 5}} \cr & {\text{Squaring the both sides}} \cr & \Rightarrow {\left( {\frac{a}{b}} \right)^2}{\text{ + }}{\left( {\frac{b}{a}} \right)^2} + 2 \times \frac{a}{b} \times \frac{b}{a} = 25 \cr & \Rightarrow \frac{{{a^2}}}{{{b^2}}}{\text{ + }}\frac{{{b^2}}}{{{a^2}}} = 25 - 2 \cr & \Rightarrow \frac{{{a^2}}}{{{b^2}}}{\text{ + }}\frac{{{b^2}}}{{{a^2}}} = 23 \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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