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What will be 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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answer is A.

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Detailed Solution

Given,
x=4, y=3 and z=2
We have to find the value of

4 x 2 + y 2 + 25 z 2 + 4 x y − 10 y z − 20 z x

.
We know that,

a + b − c 2 = a 2 + b 2 + c 2 + 2 a b − 2 b c − 2 c a

Substituting the values of x, y, and z, we get,

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 × 2 × x y − 2 × y × 5 z − 2 × 5 z × 2 x

= 2 x + y − 5 z 2

Substituting the values of x = 4, y = 3, and z = 2 in the above equation:

= (2 × 4 + 3 − 5 × 2) 2 = (8 + 3 − 10) 2 = (11 − 10) 2 = 1

So, 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

is 1.
Therefore, option 1 is correct.

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