Question

if X2+1/X2 =27 find X+1/X and x-1/X
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Answer 1

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Secondary School Math 8 points

If x 2 +1/x 2 =27, find x-1/x.

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Answers

vsks2403

vsks2403 Ambitious

x^{2} + \frac{1}{ x^{2} } = 27 

x^{2} + \frac{1}{ x^{2} } + 2 (x) ( \frac{1}{x}) - 2 (x)( \frac{1}{x} ) = 27
 
x^{2} + ( \frac{1}{ x^{2} } + 2 ( x - \frac{1}{x} = 27

(x - 1/ x )^{2} = 27 -2 

( x - 1/x)^{2} + \sqrt{25}

x - 1/x = + or - 5

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vsks2403

ans is + or - 5

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mindfulmaisel Ace

The value of \bold{x-\frac{1}{x} \text { is } 5}.

To find:

Find x-\frac{1}{x}

Solution:

Given: x^{2}+\frac{1}{x^{2}}=27

We know that (a-b)^{2}=a^{2}+b^{2}-2 a b

Putting a=x, b=\frac{1}{x}

\left(x-\frac{1}{x}\right)^{2}

=x^{2}+\frac{1}{x^{2}}-2 \times x \times \frac{1}{x}

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

=27-2\ (Given\ that\ x^{2}+\frac{1}{x^{2}}=27)

=25

Hence, \left(x-\frac{1}{x}\right)^{2}=25

\left(x-\frac{1}{x}\right)^{2}=(5)^{2}

Taking square root of both sides, we get