Find the square root of following polynomial $4 x^{2} + 9 y^{2} + 25 z^{2} - 12 x y + 30 y z - 20 z x$

| 2 x - 3 y - 5 z |

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| 2 x - 3 y + 5 z |

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| 2 x + 3 y - 5 z |

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None of these

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Solution

The correct option is A $| 2 x - 3 y - 5 z |$
We find the square root of $4 x^{2} + 9 y^{2} + 25 z^{2} - 12 x y + 30 y z - 20 z x$ as shown below:

$= \sqrt{4 x^{2} + 9 y^{2} + 25 z^{2} - 12 x y + 30 y z - 20 z x}$

$= \sqrt{(2 x)^{2} + (3 y)^{2} + (5 z)^{2} - (2 \times 2 x \times 3 y) + (2 \times 3 y \times 5 z) - (2 \times 5 z \times 2 x)}$

$= \sqrt{(2 x - 3 y - 5 z)^{2}} (∵ (a - b - c)^{2} = a^{2} + b^{2} + c^{2} - 2 a b - 2 b c - 2 c a)$

$= \pm (2 x - 3 y - 5 z)$

$= | 2 x - 3 y - 5 z |$

Hence, the square root of $4 x^{2} + 9 y^{2} + 25 z^{2} - 12 x y + 30 y z - 20 z x$ is $| 2 x - 3 y - 5 z |$ .

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(4 x^{2} + 9 y^{2} + 25 z^{2} + 6 x y + 15 y z - 10 x z)

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

Factorise:
$4 x^{2} + 9 y^{2} + 25 z^{2} + 12 x y + 30 y z + 20 z x$

{(2 x - 3 y)}^{3} + {(3 y - 5 z)}^{3} + {(5 z - 2 x)}^{3}

3 x - 7 y + 5 z = 3; 3 x + y + 5 z = 7

2 x + 3 y + 5 z = 5

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