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प्रश्न
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
उत्तर
From given problem we have to find the value of `64x^3 - 125z^3`
Given `(4x- 5z) = 16,xz = 12`
On cubing both sides of `(4x- 5z) = 16 ` we get
`(4x- 5z^3) = (16)^3`
We shall use identity `(a-b)^3 = a^3 - b^3 - 3ab(a-b)`
`4x^3 - 125z^3 - 3 (4x)(5z)(4x-5z) = 16 xx 16 xx16`
`64x^3 - 125z^3 - 60(xz) (16) = 4096`
`64x^3- 125z^3 - 60(12)(16) = 4096`
`64x^3 - 125z^3 - 11520 = 4096`
`64x^3 - 125z^3 = 4096 +11520`
`64x^3 - 125z^3 =15616 `
Hence the value of `64x^3 - 125z^3` is . 15616.
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