Find the value of $64x^3 – 125z^3$, if $4x – 5z = 16$ and $xz = 12$.

Given:

$4x – 5z = 16$ and $xz = 12$.

To do:

We have to find the value of $64x^3 – 125z^3$.

Solution:

$4x - 5z = 16$

Cubing both sides, we get,

$(4x - 5z)^3 = (16)^3$

$(4x)^3 - (5y)^3 - 3 \times 4x \times 5z(4x - 5z) = 4096$

$64x^3 - 125z^3 - 3 \times 4 \times 5xz(4x - 5z) = 4096$

$64x^3 - 125z^3 - 60 \times 12 \times 16 = 4096$

$64x^3 - 125z^3 - 11520 = 4096$

$64x^3 - 125z^3 = 4096 + 11520$

$64x^3 - 125z^3 =  15616$

The value of $64 x^{3}-125 z^{3}$ is $15616$.  

Tutorialspoint

Updated on: 10-Oct-2022

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