Advertisements
Advertisements
Question
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
Advertisements
Solution
R.H.S.
= `1/2(x + y + z)[(x - y)^2 + (y - z)^2 + (z - x)^2]`
= `1/2(x + y + z)[(x^2 + y^2 - 2xy) + (y^2 + z^2 - 2yz) + (z^2 + x^2 - 2zx)]`
= `1/2(x + y + z)(x^2 + y^2 + y^2 + z^2 + z^2 + x^2 - 2xy - 2yz - 2zx)`
= `1/2 (x + y + z)[2(x^2 + y^2 + z^2 - xy - yz - zx)]`
= `2 xx 1/2 xx (x + y + z)(x^2 + y^2 + z^2 − xy − yz − zx)`
= (x + y + z)(x2 + y2 + z2 − xy − yz − zx)
= x3 + y3 + z3 − 3xyz
= L.H.S.
Hence, it is verified.
APPEARS IN
RELATED QUESTIONS
Factorise the following using appropriate identity:
9x2 + 6xy + y2
Verify:
x3 – y3 = (x – y) (x2 + xy + y2)
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Simplify the following product:
(x2 + x − 2)(x2 − x + 2)
Evaluate the following:
(98)3
Evaluate of the following:
933 − 1073
If \[x + \frac{1}{x} = 2\], then \[x^3 + \frac{1}{x^3} =\]
Find the square of 2a + b.
The number x is 2 more than the number y. If the sum of the squares of x and y is 34, then find the product of x and y.
Use the direct method to evaluate :
(2+a) (2−a)
Evaluate: (4 − ab) (8 + ab)
Expand the following:
(2p - 3q)2
Simplify by using formula :
(2x + 3y) (2x - 3y)
If `"a" + 1/"a" = 6;`find `"a" - 1/"a"`
If p + q = 8 and p - q = 4, find:
p2 + q2
Simplify:
(4x + 5y)2 + (4x - 5y)2
Evaluate the following :
7.16 x 7.16 + 2.16 x 7.16 + 2.16 x 2.16
Using suitable identity, evaluate the following:
101 × 102
Expand the following:
(4a – b + 2c)2
Expand the following:
`(4 - 1/(3x))^3`
