Question

X²+1/x²=6
Find x+1/x=?
(x+1/x)²

Answer 1

Step-by-step explanation:

(x+1/x)^2 = x^2+2×x×1/x+1/x^2

= 6+2

= 8

x+1/x =

$\sqrt{8}$

Answer 2

Given

• x² + 1/x² = 6
• x + 1/x = ?
• (x + 1/x)² = ?

Explanation

Let x + 1/x be x

Then, ${\sf{ x + \dfrac{1}{x} = x }}$

Now, We can use this Quantity as to modify our Solution as:-

$\maltese {\large{\pmb{\boxed{\sf{ \left( x + \dfrac{1}{x} \right)^2 = x^2 + \dfrac{1}{x^2} + 2 \times x \times \dfrac{1}{x} }}}}} \\ \\ \\ \colon\implies{\sf{ ( x )^2 = x^2 + \dfrac{1}{x^2} + 2 \times \cancel{x} \times \dfrac{1}{ \cancel{x} } }} \\ \\ \\ \colon\implies{\sf{ x^2 = \left( x^2 + \dfrac{1}{x^2} \right) + 2 }} \\ \\ \\ \colon\implies{\sf{ x^2 = 6 + 2 }} \\ \\ \\ \colon\implies{\sf{ x^2 = 8 }} \\ \\ \\ \colon\implies{\sf{ x = \sqrt{8} }} \\ \\ \\ \colon\implies{\sf{ x = 2 \sqrt{2} }} \\ \\ \\ \colon\implies{\sf\large\red{ \left( x + \dfrac{1}{x} = 2 \sqrt{2} \right) }}$

• x + 1/x= 2√2
• (x + 1/x)² = (2√2)² = 8

Hence Proved !!