Question

If x^24 + 1 / x^12 = 7 then the value of x^72 + 1 / x^36 is

Answer 1

(x24 + 1)/x12 = 7

x24/x12 + 1/ x12 = 7

x12 + 1/x12 = 7. ……………. (1)

Cube on both sides,

(x12 + 1/ x12)3 = 7^3

(x12)3 + (1/x12)3 + 3 (x12 + 1/x12) = 7^3

x36 + 1/x36 + 3 x 7 = 343 (from equation 1)


x36 + 1/x36 = 343 – 21

x36 + 1/x36 = 322