Question

Identity: if x+1/x=5,find x 2 +1/x 2 ?

Answer 1

3/2.....................

Answer 2

Answer:

Given that,

$\implies x + \dfrac{1}{x} = 5$

Squaring on both sides we get:

$\implies (x+\dfrac{1}{x})^2 = (5)^2\\\\\\\implies x^2 + \dfrac{1}{x^2} + 2 \times x \times \dfrac{1}{x} = 25\\\\\\\implies x^2 + \dfrac{1}{x^2} + 2 = 25\\\\\\\implies x^2 + \dfrac{1}{x^2} = 25 - 2\\\\\\\implies \boxed{ \bf{ x^2 + \dfrac{1}{x^2} = 23}}$

Hence 23 is the required answer.