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
Write in the expanded form:
`(m + 2n - 5p)^2`
Evaluate of the following:
(9.9)3
Evaluate of the following:
(598)3
Evaluate of the following:
1043 + 963
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{7} + \frac{y}{3} \right) \left( \frac{x^2}{49} + \frac{y^2}{9} - \frac{xy}{21} \right)\]
If \[x^3 + \frac{1}{x^3} = 110\], then \[x + \frac{1}{x} =\]
If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =
If a2 + b2 + c2 − ab − bc − ca =0, then
If 49a2 − b = \[\left( 7a + \frac{1}{2} \right) \left( 7a - \frac{1}{2} \right)\] then the value of b is
Find the square of 2a + b.
Evaluate: 203 × 197
Expand the following:
(3x + 4) (2x - 1)
Simplify by using formula :
(2x + 3y) (2x - 3y)
Simplify by using formula :
(x + y - 3) (x + y + 3)
Evaluate, using (a + b)(a - b)= a2 - b2.
999 x 1001
Simplify:
(3x + 5y + 2z)(3x - 5y + 2z)
Simplify:
(3a - 7b + 3)(3a - 7b + 5)
Expand the following:
(3a – 2b)3
If a + b + c = 5 and ab + bc + ca = 10, then prove that a3 + b3 + c3 – 3abc = – 25.
