Question

If x+1/x=4, then calculate the value of x^2+1/x^2.

Answer 1

your ans

given:-

x+1/x=4

to find:-

x2+1/x2

use formula:-

(x+1/x)2=x2+1/x2+2

(4)2=x2+1/x2+2

16-2=x2+1/x2

x2+1/x2=14

Answer 2

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Heya

Given :-

x + 1/x = 4

To find :-

x^2 + 1/x^2 = ?

Solution :-

$x + \frac{1}{x} = 4 \\ \\ squaring \: both \: sides \\ \\ {(x + \frac{1}{x} )}^{2} = {4}^{2} \\ \\ {(x)}^{2} + {( \frac{1}{x} )}^{2} + 2 \times x \times \frac{1}{x} = 16 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 16 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 16 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 14$

Identity used :-

(a + b)^2 = a^2 + b^2 + 2ab

Hope this helps you.