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Question
If 3x + 4y = 16 and xy = 4; find the value of 9x2 + 16y2.
Solution
Given that ( 3x + 4y ) = 16 and xy = 4
We need to find 9x2 + 16y2.
We know that
( a + b )2 = a2 + b2 + 2ab
Consider the square of 3x + 4y :
∴ ( 3x + 4y )2 = (3x)2 + (4y)2 + 2 x 3x x 4y
⇒ ( 3x + 4y )2 = 9x2 + 16y2 + 24xy .....(1)
Substitute the values of ( 3x + 4y ) and xy
in the above equation (1), we have
( 3x + 4y )2 = 9x2 + 16y2 + 24xy
⇒ (16)2 = 9x2 + 16y2 + 24(4)
⇒ 256 = 9x2 + 16y2 + 96
⇒ 9x2 + 16y2 = 160
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