Find the value of 64x3


Find the value of $64 x^{3}-125 z^{3}$, if $4 x-5 z=16$ and $x z=12$


Given, $64 x^{3}-125 z^{3}$

Here, $4 x-5 z=16$ and $x z=12$

Cubing $4 x-5 z=16$ on both sides

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

We know that, $(a-b)^{3}=a^{3}-b^{3}-3 a b(a-b)$

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

$64 x^{3}-125 z^{3}-60(x z)(16)=4096$

$64 x^{3}-125 z^{3}-60(12)(16)=4096$

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

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

$64 x^{3}-125 z^{3}=15616$

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

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