Advertisements
Advertisements
Question
Without actually calculating the cubes, find the value of:
`(1/2)^3 + (1/3)^3 - (5/6)^3`
Advertisements
Solution
Given, `(1/2)^3 + (1/3)^3 - (5/6)^3` or `(1/2)^3 + (1/3)^3 + (- 5/6)^3`
Here, we see that,
`1/2 + 1/3 - 5/6`
= `(3 + 2 - 5)/6`
= `(5 - 5)/6`
= 0
∴ `(1/2)^3 + (1/3)^3 - (5/6)^3 = 3 xx 1/2 xx 1/3 xx (-5/6)` ...[Using identity, if a + b + x = 0, then a3 + b3 + c3 = 3abc]
= `- 5/12`
APPEARS IN
RELATED QUESTIONS
Use suitable identity to find the following product:
`(y^2+3/2)(y^2-3/2)`
Expand the following, using suitable identity:
(2x – y + z)2
Evaluate the following using suitable identity:
(99)3
If 2x + 3y = 8 and xy = 2 find the value of `4x^2 + 9y^2`
Write in the expanded form: (-2x + 3y + 2z)2
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
Find the following product:
(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to ______.
If a1/3 + b1/3 + c1/3 = 0, then
The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to
If x + y = `7/2 "and xy" =5/2`; find: x - y and x2 - y2
Use the direct method to evaluate the following products:
(a – 8) (a + 2)
Use the direct method to evaluate :
(3b−1) (3b+1)
Use the direct method to evaluate :
(4+5x) (4−5x)
Expand the following:
`(2"a" + 1/(2"a"))^2`
Simplify:
(x + y - z)2 + (x - y + z)2
Simplify:
`(x - 1/x)(x^2 + 1 + 1/x^2)`
Simplify:
(3x + 5y + 2z)(3x - 5y + 2z)
Factorise the following:
9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz
Without actually calculating the cubes, find the value of:
(0.2)3 – (0.3)3 + (0.1)3
