Question

If x+1÷x=8,Find the value of x square + 1÷x square​

Answer 1

Answer:

(x+1/x )=8

squaring both sides

using (a+b)^2 for lhs

x^2 +1/x^2 +2(x*1/x) =64

x^2+1/x^2=64-2=62

Step-by-step explanation:

Answer 2

Given:

x+$\frac{1}{x}$=8

To find:

$x^{2}+ \frac{1}{x^{2} }$

Solution:

x+$\frac{1}{x}$=8

square both side

(x+$\frac{1}{x}$)²=8²

expand by the using algebraic identity

(a+b)²=a²+b²+2ab

x²+$\frac{1}{x^{2} }$+2=64    (∵x×$\frac{1}{x}$=1)

solve

x²+$\frac{1}{x^{2} }$=64-2

x²+$\frac{1}{x^{2} }$=62

Hence, x²+$\frac{1}{x^{2} }$=62