Question

If (Ax + By - Cz)2 = 4x2+ 3y2+ 2z2+ $4\sqrt{3xy}$-$2\sqrt{6yz}$ - 4√2xz, then find the value of A2+ B2C2.

• A. 16
• B. 8
• C. 12
• D. 10

Answer 1

Answer: (D)

10

Answer 2

The correct option is (D): 10.
(a + b + c)2 = a2+ b2+ c2+ 2ab + 2bc + 2ca
(Ax + By - Cz)2 = 4x2+ 3y2+ 2z2+ 4$\sqrt3$xy - $\sqrt2$6yz - 4√2xz
(Ax + By - Cz)2 = (2x)2 + ($\sqrt3$y)2 + ( - $\sqrt2$z)2 + 2 * 2x * $\sqrt3$y + 2 * $\sqrt3$y* ( -$\sqrt2$z) + 2 * 2x * ( - $\sqrt2$z)
(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.