Question

if x + 1/x =8 ,find the value of x² + 1/x².​

Answer 1

Given :

x + 1/x = 8

To Find :

x² + 1/x²

Solution :

Analysis :

Here by using the required identity we can find the answer.

Required Formula :

(a + b)² = a² + 2ab + b²

Explanation :

Using the formula (a + b)² = a² + 2ab + b²,

where,

• a = x
• b = 1/x

Using the formula and substituting the required values,

$\\ :\implies\sf x+\dfrac{1}{x}=8$

$\\ :\implies\sf \left({x+\dfrac{1}{x}}\right)^2=x^2+2.x.\dfrac{1}{x}+\dfrac{1}{x^2}$

$\\ :\implies\sf (8)^2=x^2+2.\not{x}.\dfrac{1}{\not{x}}+\dfrac{1}{x^2}$

$\\ :\implies\sf 64=x^2+2.1+\dfrac{1}{x^2}$

$\\ :\implies\sf 64=x^2+2+\dfrac{1}{x^2}$

$\\ :\implies\sf 64-2=x^2+\dfrac{1}{x^2}$

$\\ :\implies\sf 62=x^2+\dfrac{1}{x^2}$

$\\ \therefore\boxed{\bf x^2+\dfrac{1}{x^2}=62.}$

The value of x² + 1/x² is 62.

Explore More :

• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)² + (a - b)² = 2(a² + b²)
• (a + b)² - (a - b)² = 4ab
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
• (x + a)(x + b)(x + c) = x³ + (a + b + c)x² + (ab + bc + ca)x + abc

Answer 2

Step-by-step explanation:

C O M E

ON M E E T

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