Question

$3x + 4y = 16 \: \: \: xy = 4 \\ find \: the \: value \: of \: 9x^2 + 16y ^2$
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Answer 1

Answer:

160

Step-by-step explanation:

Given------> 3x + 4y = 16 and xy = 4

To find------> 9x² + 16y² = ?

Solution------> ATQ ,

3x + 4y = 16 and xy = 4

3x + 4y = 16

Squaring both sides we get,

=> ( 3x + 4y )² = ( 16 )²

We know that ,

( a + b )² = a² + b² + 2ab , applying it we get,

=> ( 3x )² + ( 4y )² + 2 ( 3x ) ( 4y ) = 256

=> 9x² + 16 y² + 24 xy = 256

=> ( 9x² + 16 y² ) + 24 ( xy ) = 256

Putting xy = 4 , in it we get,

=> ( 9x² + 16y² ) + 24 ( 4 ) = 256

=> ( 9x² + 16y² ) + 96 = 256

=> ( 9x² + 16y² ) = 256 - 96

=> ( 9x² + 16y² ) = 160