Question

if x+1/x = 3,find x²+1/x²​

Answer 1

Required Answer:-

Given:

• x + 1/x = 3

To find:

• The value of x² + 1/x²

Solution:

★ We will use the identity (a + b)² = a² + 2ab + b² to find the value of x² + 1/x². Here is the solution.

We have,

$\rm \implies \bigg(x + \dfrac{1}{x} \bigg) = 3$

Squaring both sides, we get,

$\rm \implies \bigg(x + \dfrac{1}{x} \bigg)^{2} = {3}^{2}$

Now, applying the identity, we get,

$\rm \implies {x}^{2} + \dfrac{1}{{x}^{2} }+ 2 \times \cancel{x} \times \dfrac{1}{ \cancel{x}} = {3}^{2}$

$\rm \implies {x}^{2} + \dfrac{1}{x^{2} }+ 2 = 9$

$\rm \implies {x}^{2} + \dfrac{1}{x^{2}} = 9 - 2$

$\rm \implies {x}^{2} + \dfrac{1}{x^{2}} = 7$

★ Hence, the value of x² + 1/x² is 7.

Answer:

• The value of x² + 1/x² is 7.

More Identities:

• (a - b)² = a² - 2ab + b²
• (a + b)² = (a - b)² + 4ab
• (a - b)² = (a + b)² - 4ab
• a² - b² = (a + b)(a - b)