Question

If x - 1/x = 1/2, then find the value of 4 x^2 + 4/x^2

Answer 1

In the above Question , the following information is given -

x - 1 / x = 4

To find -

Find the value of 4x² + 4 / x² .

Solution -

Here ,

x - 1 / x = 4

Squaring both sides -

=> x² + 1 / x² + 2 = 4

=> x² + 1 / x² = 2

Multiplying 4 on both sides -

=> 4 [ x² + 1 / x² ] = 2 × 4 = 8

=> 4 [ x² + 1 / x² ] = 8

=>4 x² + 4 / x² = 8 .

Thus , the required value is 8 .

This is the answer .

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Additional Information -

( a + b )² = a² + 2ab + b²

( a - b )² = a² - 2ab + b²

(a + b)( a - b ) = a² - b²

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