Question

if a/b+b/a=10 then find the value of (a/b)^10+(b/a)^10

Answer 1

✔✔heya here is ur answer ☺☺

THANK YOU ✌✌

HOPE IT HELPS YOU ☺☺

Answer 2

Given $\frac{a}{b} +\frac{b}{a} =10$. Square both sides of the equation,

$(\frac{a}{b} +\frac{b}{a})^2 =10^2\\ (\frac{a}{b})^2 +(\frac{b}{a})^2 +2=100\\ (\frac{a}{b})^2 +(\frac{b}{a})^2=98$

Again square both the sides,

$(\frac{a}{b})^4 +(\frac{b}{a})^4+2=98^2\\ (\frac{a}{b})^4 +(\frac{b}{a})^4=9602$

Again square both the sides,

$(\frac{a}{b})^8 +(\frac{b}{a})^8+2=9602^2\\ (\frac{a}{b})^8 +(\frac{b}{a})^8=92198402$

Now,

$[(\frac{a}{b})^8 +(\frac{b}{a})^8] [ (\frac{a}{b})^2 +(\frac{b}{a})^2]=92198402*98\\ (\frac{a}{b})^{10} +(\frac{b}{a})^{10}+(\frac{a}{b})^6 +(\frac{b}{a})^6=92198402*98\\ (\frac{a}{b})^{10} +(\frac{b}{a})^{10}+[(\frac{a}{b})^4 +(\frac{b}{a})^4][(\frac{a}{b})^2 +(\frac{b}{a})^2]-[(\frac{a}{b})^2 +(\frac{b}{a})^2]=92198402*98$

$(\frac{a}{b})^{10} +(\frac{b}{a})^{10}+[9602][98]-98=92198402*98\\ (\frac{a}{b})^{10} +(\frac{b}{a})^{10}=9,034,502,498$