Question:
If (Ax + By - Cz)2 = 4x2+ 3y2+ 2z2+ \(4\sqrt{3xy} \)-\( 2\sqrt{6yz}\) - 4√2xz, then find the value of A2+ B2C2.
If (Ax + By - Cz)2 = 4x2+ 3y2+ 2z2+ \(4\sqrt{3xy} \)-\( 2\sqrt{6yz}\) - 4√2xz, then find the value of A2+ B2C2.
Updated On: Sep 10, 2024
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The Correct Option is D
Solution and Explanation
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.
(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.
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