Advertisements
Advertisements
Question
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
Advertisements
Solution
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.
APPEARS IN
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
104 × 96
Write the following cube in expanded form:
(2a – 3b)3
Evaluate the following using identities:
(2x + y) (2x − y)
Write in the expanded form:
(2a - 3b - c)2
Write the expanded form:
`(-3x + y + z)^2`
Write in the expanded form:
`(m + 2n - 5p)^2`
Evaluate of the following:
463+343
Evaluate of the following:
933 − 1073
If a + b = 6 and ab = 20, find the value of a3 − b3
If x = −2 and y = 1, by using an identity find the value of the following
If a + b + c = 9 and a2+ b2 + c2 =35, find the value of a3 + b3 + c3 −3abc
If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =
If a1/3 + b1/3 + c1/3 = 0, then
Evaluate: (4 − ab) (8 + ab)
Expand the following:
(3x + 4) (2x - 1)
Simplify:
(x + y - z)2 + (x - y + z)2
Simplify:
`(x - 1/x)(x^2 + 1 + 1/x^2)`
Simplify:
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)
Expand the following:
(4a – b + 2c)2
Factorise the following:
25x2 + 16y2 + 4z2 – 40xy + 16yz – 20xz
