Compute the value of 9x^2 + 4y^2 if xy = 6 and 3x + 2y = 12.​

Compute the value of 9x^2 + 4y^2 if xy = 6 and 3x + 2y = 12.​

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  1. Answer:

    Consider the equation 3x + 2y = 12

    Now, square both sides:

    (3x + 2y)^2 = 122

    => 9x^2 + 12xy + 4y^2 = 144

    =>9x^2 + 4y^2 = 144 – 12xy

    From the questions, xy = 6

    So,

    9x^2 + 4y^2 = 144 – 72

    Thus, the value of 9x^2 + 4y^2 = 72

    Answered by GAUTHMATH

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