Find the value of 64x³ – 125z³, if 4x – 5z = 16 and xz=12.
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Given : 4x – 5z = 16 and xz = 12
To find : value of 64x³ – 125z³
Solution :
By using the identity, (a - b)³ = a³ - b³ - 3ab(a - b)
On cubing 4x – 5z = 16 both sides,
(4x – 5z)³ = 16³
(4x)³ - (5y)³ - 3( 4x )(5z) (4x - 5z) = 4096
64x³ - 125y³ - 60xz(4x - 5z) = 4096
64x³ - 125y³ - 60 x 12 x 16 = 4096
[xz = 12]
64x³ - 125y³ - 11520 = 4096
64x³ - 125y³ = 4096 + 11520
64x³ - 125y³ = 15616
Hence the value of 64x³ - 125y³ is 15616.
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