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Question
Find the value of 4x2 + y2 + 25z2 + 4xy − 10yz − 20zx when x = 4, y = 3 and z = 2.
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Solution
We have,
`4x^2 + y^2 + 25z^2 + 4xy - 10yz - 20zx`
`=> (2x)^2 + (y)^2 + (-5z)^2 + 2(2x)(y) + 2(y)(-5z) + 2(-5z)(2x)`
`=:> (2x + y - 5z)^2`
`=> [2[4] + 3 - 5(2)]^2` [∵ x = 4, y = 3 and z = 2]
`= [8 + 3 - 10]^2`
`=[1]^2`
= 1
`∴ 4x^2 + y^2 + 25z^2 + 4xy - 10yz - 20zx = 1`
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