Question

find the value of 64xcube-125zcube if​

Answer 1

Answer:

$4x - 5z = 16 \\ cubing \: both \: the \: sides \\ 64{x}^{3} - 125 {z}^{3} = 4096 \\ \\ 4x - 5z = 3 \div 5 \\ cubing \: both \: sides \\ 64 {x}^{3} - 125 {z}^{3} = \frac{27}{125}$

HOPE IT HELPS YOU :)

Answer 2

As we know that :

a³ - b³ = (a-b)³+3ab(a-b)

Such as :

64x³-125z³

=> (4x)³-(5z)³ = (4x-5z)³+3(4x.5z)(4x-5z)

=> 64x³-125z³ = (4x-5z)³+60xz(4x-5z)

(1) (4x-5z) = 16 and xz = 12

=> 16³+60×12×16 = 15616

(2) (4x-5z) = 3/5 and xz = 6

=> 27/125+60×6×3/5 = 27/125+216

=> 27027/125 = 216.216

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