If x-1 x-20- find the value of x 2-1 x 2-

Let us consider the following equation: x+1x=20 Squaring both sides, we get: x+1x2=202=400 #8658;x+1x2=400 #8658;x2+2 #215;x #215;1x+1x2=400 #160; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Solving a Quadratic Equation by Factorization Method

If x+1 x=20, ...

Question

If $x + \frac{1}{x} = 20,$ find the value of $x^{2} + \frac{1}{x^{2}} .$

Open in App

Solution

Let us consider the following equation:

$x + \frac{1}{x} = 20$
Squaring both sides, we get:

${(x + \frac{1}{x})}^{2} = {(20)}^{2} = 400 \Rightarrow {(x + \frac{1}{x})}^{2} = 400 \Rightarrow x^{2} + 2 \times x \times \frac{1}{x} + {(\frac{1}{x})}^{2} = 400 [(a + b)^{2} = a^{2} + b^{2} + 2 a b] \Rightarrow x^{2} + 2 + \frac{1}{x^{2}} = 400$
$\Rightarrow x^{2} + \frac{1}{x^{2}} = 398$ (Subtracting 2 from both sides)

Thus, the answer is 398.

Suggest Corrections

Similar questions

Q. If

x + \frac{1}{x} = 11,

find the value of

x^{2} + \frac{1}{x^{2}}

Q. If

x - \frac{1}{x} = - 1

, find the value of

x^{2} + \frac{1}{x^{2}}

Q. If

x^{2} + \frac{1}{x^{2}} = 18,

find the values of

x + \frac{1}{x} and x - \frac{1}{x} .

Q. If

x = 3 - 2 \sqrt{2}

, find the value of:
i)

\frac{1}{x}

ii)

x + \frac{1}{x}

iii)

x - \frac{1}{x}

iv)

\sqrt{x} + \frac{1}{\sqrt{x}}

\sqrt{x} - \frac{1}{\sqrt{x}}

vi)

x^{2} + \frac{1}{x^{2}}

vii)

x^{2} - \frac{1}{x^{2}}

Q. If

x + \frac{1}{x} = \sqrt{5}

, find the value of

x^{2} + \frac{1}{x^{2}}

and

x^{4} + \frac{1}{x^{4}}

Join BYJU'S Learning Program

If x+1x=20, find the value of x2+1x2.

Let us consider the following equation: x+1x=20 Squaring both sides, we get: x+1x2=202=400⇒x+1x2=400⇒x2+2×x×1x+1x2=400 [(a+b)2=a2 +b2 +2ab]⇒x2+2+1x2=400 ⇒x2+1x2=398 (Subtracting 2 from both sides) Thus, the answer is 398.

If $x + \frac{1}{x} = 20,$ find the value of $x^{2} + \frac{1}{x^{2}} .$