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Question -

Find the value of 64x3 тАУ 125z3, if 4x тАУ 5z = 16 and xz = 12.



Answer -

4x тАУ 5z = 16, xz = 12
Cubing both sides,
(4x тАУ 5z)3┬а= (16)3
тЗТ (4x)3┬атАУ(5y)3┬атАУ 3 x 4x x 5z(4x тАУ 5z) = 4096
тЗТ 64x3┬атАУ125z3┬атАУ 3 x 4 x 5 x xz(4x тАУ 5z) = 4096
тЗТ┬а64x3┬атАУ 125z3┬атАУ 60 x 12 x 16 = 4096
тЗТ 64x3┬атАУ125z3┬атАУ 11520 = 4096
тЗТ┬а64x3┬атАУ 125z3┬а= 4096 + 11520 = 15616

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