1.

If 3√3x3 + 2√2y3 – 8z3 + 6√6xyz = (Ax + By – Cz)(3x2 + 2y2 + 4z2 – √2Axy + 2Byz + 2√3Zx), find the value of A2 + B2 – C2?1. 42. 13. 94. 5

Answer» Correct Answer - Option 2 : 1

Given:

3√3x3 + 2√2y3 – 8z3 + 6√6xyz = (Ax + By – Cz)(3x2 + 2y2 + 4z2 – √2Axy + 2Byz + 2√3Zx)

Concept:

Compare the unknown values of the given equation with the actual values of the equation after expansion.

Formula used:

a3 + b3 + c3 – 3abc = (a + b + c)[a2 + b2 + c2 – (ab + bc + ca)]

Calculation:

∵ 3√3x3 + 2√2y3 – 8z3 + 6√6xyz = (√3x)3 + (√2y)3 + (–2z)3 – 3(√3x)(√2y)( –2z)

∴ (√3x)3 + (√2y)3 + (-2z)3 – 3(√3x)(√2y)(-2z) = (√3x + √2y – 2z)[3x2 + 2y2 + 4z2 – (√3x)(√2y) – (√2y)( –2z) – (√3x)(–2z)]

⇒ (√3x)3 + (√2y)3 + (-2z)3 – 3(√3x)(√2y)(-2z) = (√3x + √2y – 2z)[3x2 + 2y2 + 4z2 – (√3x)(√2y) + (√2y)(2z) + (√3x)(2z)]

∴ If we compare the values of the equations;

We get

A = √3

B = √2

C = 2

∴ A2 + B2 – C2 = (√3)2 + (√2)2 – (2)2

= 3 + 2 – 4

= 5 – 4

= 1


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