Find the value of $4 x^{2} + y^{2} + 25 z^{2} + 4 x y - 10 y z - 20 z x$ when x = 4, y = 3 and z = 2.

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Solution

x = 4, y = 3, z = 2

$\Rightarrow 4 x^{2} + y^{2} + 25 z^{2} + 4 x y - 10 y z - 20 z x = (2 x)^{2} + (y)^{2} + (5 z)^{2} + 2 \times 2 x \times y - 2 \times y \times 5 z - 2 \times 5 z \times 2 x = (2 x + y - 5 z)^{2} = (2 \times 4 + 3 - 5 \times 2)^{2} = (8 + 3 - 10)^{2} = (11 - 10)^{2} = (1)^{2} = 1$

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4 x^{2} + 9 y^{2} + 25 z^{2} - 12 x y - 30 y z + 20 z x

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4 x^{2} + 9 y^{2} + 25 z^{2} + 12 x y - 30 y z - 20 z x

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