Question

If x+1/x =7, then find x² + 1/x²​

Answer 1

Question : If x+1/x =7, then find x² + 1/x²

SOLUTION :

Given,

x + 1/x = 7

TO FIND :

x² + 1/x²

Step - by - step Explanation :

x + 1/x = 7

Squaring on both sides.

(x + 1/x)² = (7)²

We know that,

(a + b)² = a² + 2ab + b²

(x)² + 2(x)(1/x) + (1/x)² = 49

x² + 2x/x + 1/x² = 49

x² + 2 + 1/x² = 49

x² + 1/x² = 49 - 2

x² + 1/x² = 47

Therefore, x² + 1/x² = 47

Answer 2

x + 1/x = 7
Square both sides
(x+1/x)^2 = 7^2
x^2+1/x^2 +2(x into 1/x) = 49
x^2+1/x^2= 49-2 = 47