The value of $9 x^{2} + 49 y^{2} - 42 x y$ when $x = 15$ and $y = 3$ is ___________.

636

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576

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456

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386

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Solution

The correct option is B $576$
Given expression is $f (x, y) = 9 x^{2} + 49 y^{2} - 42 x y$
We need to find value of expression at $x = 15, y = 3$
$f (15, 3) = [9 \times (15)^{2}] + [49 \times (3)^{2}] - [42 \times 15 \times 3]$
$= [9 \times 225] + [49 \times 9] - [42 \times 45]$
$= 2025 + 441 - 1890$
$= 576$

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9 x^{2} + 49 y^{2} - 42 x y

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