Question

If 4x^2 + 9y^2 = 13 and xy = 1. Find (2x + 3y)

Answer 1

In the above Question , the following information is given -

4x² + 9y² = 13 and xy = 1 .

To find -

Find the value of 2x + 3y.

Solution -

4x² + 9y² = 13

=> 4x² + 9y² + 12 = 13 + 12

=> 4x² + 12 + 9y² = 25 .

Now , xy = 1.

So,

=> 4x² + 12xy + 9y² = 25

=> ( 2x )² + 2 ( 2x )( 3y ) + ( 3y )² = 25

=> ( 2x + 3y ) ² = 25

=> 2x + 3y = | 5 | .

This is the required answer .

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Additional Information -

( a + b )² = a² + 2ab + b²

( a - b )² = a² - 2ab + b²

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