Question

sum of a number and its multiplicative inverse is 3
prove that
$x^{5} + \frac{1}{x ^{5} } = 123$
​

Answer 1

x + 1 / x = 3

Square above,

X^2 + 1/x^2 = 1

Multiply x + 1/x in above

(X^2 + 1/x^2) (x + 1 / x) =1*3=3

x^3 + 1/x^3 + x +1/x = 3

x^3 + 1/x^3 = 0

Square above,

x^4 + 1/x^4= - 1

Multiply x + 1/x in above

(x^4 + 1/x^4) (x + 1 / x) = (-1)*3 = -3

x^5 + 1/x^5 + x^3 + 1/x^3 = -3

x^5 + 1/x^5 = - 3

Because x^3 + 1/x^3 = 0

Answered by an IIT JEE ASPIRANT and all India mathematics OLYMPIAD TOPPER in class 10th