Question:
If (Ax + By - Cz)2 + 4\(\sqrt3\)xy - 2\(\sqrt6\)yz - 4\(\sqrt2\)xz, then find the value of A2 + B2C2.
If (Ax + By - Cz)2 + 4\(\sqrt3\)xy - 2\(\sqrt6\)yz - 4\(\sqrt2\)xz, then find the value of A2 + B2C2.
Updated On: Sep 10, 2024
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The Correct Option is D
Solution and Explanation
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.
(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.
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