Question

5x-3y=15 and xy=3 then find 25x^+16y^

Answer 1

In the above Question , the following values are given -

5x - 3y = 15 and xy = 3 .

To find -

Find the value of 25x² + 9y²

Solution -

According to the first condition -

=> 5x - 3y = 15

This is of the form , a - b

Squaring this , it results into a² - 2ab + b²

So ,

=> 25x² - 30xy + 9y² = 225

=> 25x² + 9y² = 225 + 30xy

Now , xy = 3 . So , 30xy = 30

Thus ,

=> 25x² + 9y² = 225 + 30 = 255 .

This is the required 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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