Question

if 2x^2 + 3y^2 + 4z^2 - √6xy - 2√3yz - 2√2xz = 0 , then find the value of (2x^2 + 3y^2 +16z^2 + 2√6xy - 8√3yz - 8√2xz ).​

Answer 1

Answer:

Given : 2 x 2 + 3 y 2 + 4 z 2 - 6‾√ xy - 2 3‾√ yz - 2 2‾√ xz = 0

We know : ( a + b + c )2 = a2 + b2 + c2 + 2 ab + 2 bc + 2 ca

Here , a = 2‾√ x , b = 3‾√ y and c = 2 z , So

( 2‾√ x +3‾√ y + 2 z )2 = 2 x 2 + 3 y 2 + 4 z 2 + 2 6‾√ xy + 4 3‾√ yz + 4 2‾√ xz

So,

2 x 2 + 3 y 2 + 4 z 2 - 6‾√ xy - 2 3‾√ yz - 2 2‾√ xz + 2 6‾√ xy + 4 3‾√ yz + 4 2‾√ xz = 2 6‾√ xy + 4 3‾√ yz + 4 2‾√ xz

2 x 2 + 3 y 2 + 4 z 2 + 2 6‾√ xy + 4 3‾√ yz + 4 2‾√ xz = 2 6‾√ xy + 4 3‾√ yz + 4 2‾√ xz + 6‾√ xy + 2 3‾√ yz + 2 2‾√ xz

( 2‾√ x +3‾√ y + 2 z )2 = 3 6‾√ xy + 6 3‾√ yz + 6 2‾√ xz

Answer 2

Answer:

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