Find the value of 64x3−125z3,if 4x−5z=16 and xz=12.
4x - 5z = 16, xz = 12
Cubing both sides,
(4x−5z)3=(16)3
⇒ (4x)3−(5y)3−3×4x×5z(4x−5z)=4096⇒ 64x3−125z3−3×4×5×xz(4x−5z)=4096⇒ 64x3−125z3−60×12×16=4096⇒ 64x3−125z3−11520=4096⇒ 64x3−125z3=4096+11520=15616