Question

if 3x+2y=12 and xy=6 then, find the value of 9x²+4y²?

Answer 1

9x^2+4y^×=(3x)^2+(2y)^2=(3x+4y)^2-2×3x×2y
=12^2-(12×6)
=144-72
=72

Answer 2

Hey Mate ✌

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↪ Here's your answer,

==> 3x + 2y = 12 ............(1)

==> xy = 6 .........(2)

==> y = 6/x from (2)........(3)


Now, by substituting (3) in (1)

we get,

3x + 2y = 12

==> 3x + 2(6/x) = 12

==> 3x + 12/x = 12

==> 3x² + 12 = 12x

==> 3x² - 12x +12 = 0

==> x² - 4x + 4 = 0

==> x² - 2x - 2x + 4 = 0

==> x(x - 2) - 2(x - 2) = 0

==> (x - 2)(x - 2) = 0

==> x = 2 or x = 2

therefore, by substituting x = 2 in (2)

we get,

xy = 6

==> 2y = 6

==> y = 3


therefore,

Now on substituting both x = 2 and y = 3 in 9x² + 4y²

we get,

9(2)² + 4(3)² = 36 + 36

==> 72

is the required answer.

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⭐ Hope it helps you : ) ⭐