Question

if a/b+b/a=2 then the value of (a/b)^21-(b/a)^21​

Answer 1

0

Step-by-step explanation:

given:-

$\frac{a}{b} + \frac{b}{a} = 2$

question:-

${ (\frac{a}{b} })^{21} - ( { \frac{b}{a} )}^{21}$

solution:-

$\frac{a}{b} + \frac{b}{a} = 2 \\ \\ \frac{ {a}^{2} + {b}^{2} }{ab} = 2 \\ \\ {a}^{2} + {b}^{2} = 2ab \\ \\ {a}^{2} + {b}^{2} - 2ab = 0 \\ \\ {(a - b)}^{2} = 0 \\ \\ a - b = 0 \\ a = b$

now:-

put this value in question equation-->

$({ \frac{a}{b} })^{21} - ( { \frac{b}{a} })^{21} \\ \\ ({ \frac{a}{a} )}^{21} - ( { \frac{a}{a} )}^{2} = 0$

answer = 0