Question

If (Ax + By - Cz)2 + 4$\sqrt3$xy - 2$\sqrt6$yz - 4$\sqrt2$xz, then find the value of A2 + B2C2.

• A. 16
• B. 8
• C. 12
• D. 10

Answer 1

Answer: (D)

10

Answer 2

We know that :
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(Ax + By - Cz)2 = 4x2 + 3y2 + 2z2 + 4$\sqrt3$xy - 2$\sqrt6$yz - 4$\sqrt2$xz
(Ax + By - Cz)2 = (2x)2 + ($\sqrt3$y)2 + (-$\sqrt2$z)2 + 2 * 2x * $\sqrt3$y + 2 * $\sqrt3$y * (-$\sqrt2$z) + 2 * 2x * ($\sqrt2$xz)
(Ax + By - Cz)2 = (2x + $\sqrt3$y - $\sqrt2$z)2
After comparing:
A = 2, B = $\sqrt3$ and C = $\sqrt2$
Now,
A2 + B2C2
= 22 + ($\sqrt3$)2 * ($\sqrt2$)2
= 4 + 6
= 10
So, the correct option is (D) : 10.