Question

9x square +4y sqaure,if 3x+2y=12 and xy=6

Answer 1

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Answer 2

Given, 3x + 2y = 12

Square on both sides

( 3x + 2y )^2 = 12^2

( a + b)^2 = a^2 + b^2 + 2ab

( 3x )^2 + ( 2y )^2 + 2( 3x * 2y ) = 144

9x^2 + 4y^2 + 2( 6xy ) = 144

Value of xy in question is 6

9x^2 + 4y^2 + 2{ 6( 6 ) } = 144

9x^2 + 4y^2 + 2{ 36 } = 144

9x^2 + 4y^2 + 72 = 144

9x^2 + 4y^2 = 144 - 72

9x^2 + 4y^2 = 72

Therefore the value of 9x^2 + 4y^2 satisfying the question is 72.

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