IF x2+y2+4z2-6x-2y-4z+11=0 then, xyz is equal to

x + y + 4z – 6x – 2y – 4z + 11 = 0

x + y + 4z – 6x – 2y – 4z + 9 + 1 + 1

x + y + 4z – 6x – 2y – 4z + 3 + 1 + 1

x – 6x + 3 + y – 2y – 1 + (2z) – 4z + 1

by the identities of (a-b) = a + b – 2ab,

(x-3)^2 + (y-1)^2 + (2z-1)^2=0

By the BJUH concept, A=B=C=0. WHERE A, B, AND C ARE REAL NUMBER

A = x – 3 = 0 ==> x = 3

B = y – 1 = 0 ==> y = 1

C = 2z – 1 ==> z = 1/2

ABC=3*1*1/2=3/2

HENCE, ABC = 3/2 IS THE FINAL ANSWER

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