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

Given:

$x = 4, y = 3$ and $z = 2$.

To do:

We have to find the value of $4x^2 + y^2 + 25z^2 + 4xy - 10yz - 20zx$.

Solution:

We know that,

$(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca$

Therefore,

$4x^2 + y^2 + 25z^2 + 4xy - 10yz - 20zx = (2x)^2 + (y)^2 + (5z)^2 + 2 \times 2x \times y-2 \times y \times 5z - 2 \times 5z \times 2x$

$= (2x + y- 5z)^2$

$= (2 \times 4 + 3- 5 \times 2)^2$

$= (8 + 3- 10)^2$

$= (11 - 10)^2$

$= 1^2$

$= 1$

Hence, the value of $4x^2 + y^2 + 25z^2 + 4xy - 10yz - 20zx$ is $1$.   

Tutorialspoint

Updated on: 10-Oct-2022

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