Question

solve this plz as fast as possible​

Answer 1

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$\bf {x}^{2} + \frac{1}{ {x}^{2} } = 23, \: \: x + \frac{1}{x} = ?$

$\bf\mathfrak{\color{orange}{\underline {\underline{using \: idetity}}}}$

$\large{\color{red}{(a+ b) {}^{2} = {a}^{2} + {b}^{2} + 2ab }}$

$\bf {(x + \frac{1}{x}) }^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x}$

$\bf {(x + \frac{1}{x}) }^{2} = 23 +2 \times x \times \frac{1}{x}$

$\bf{(x + \frac{1}{x}) }^{2} =23 + 2$

$\bf{(x + \frac{1}{x}) }^{2} =25$

$\bf{(x + \frac{1}{x}) }^{2} = {5}^{2}$

$\bf{(x + \frac{1}{x}) } =5$

✏Additionally

More Identities

• ${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy$

• ${(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy$

• ${x}^{2} - {y}^{2} = (x + y)(x - y)$

Answer 2

5

As x^2 + 1/x^2 is given 23 ,we need to find x + 1/x

( x + 1/x)^2 = x^2 + 1/x^2 + 2× x × 1/x

= x^2 + 1/x^2 + 2

x^2 + 1/x^2 = 23 so

x^2 + 1/x^2 + 2 = 23 + 2

= 25

( x + 1/x)^2 = 25

x + 1/x = √25

= 5