Advertisements
Advertisements
प्रश्न
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
Advertisements
उत्तर
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
संबंधित प्रश्न
Expand the following, using suitable identity:
(3a – 7b – c)2
Write the following cube in expanded form:
`[3/2x+1]^3`
if `x^2 + 1/x^2 = 79` Find the value of `x + 1/x`
Simplify the following products:
`(m + n/7)^3 (m - n/7)`
If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
Evaluate of the following:
933 − 1073
Find the following product:
(4x − 5y) (16x2 + 20xy + 25y2)
Find the following product:
If a + b = 10 and ab = 16, find the value of a2 − ab + b2 and a2 + ab + b2
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
(a − b)3 + (b − c)3 + (c − a)3 =
If \[x - \frac{1}{x} = \frac{15}{4}\], then \[x + \frac{1}{x}\] =
The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to
Evalute : `((2x)/7 - (7y)/4)^2`
If x + y = `7/2 "and xy" =5/2`; find: x - y and x2 - y2
Simplify by using formula :
(1 + a) (1 - a) (1 + a2)
If `"a" + 1/"a" = 6;`find `"a"^2 - 1/"a"^2`
If `x + (1)/x = 3`; find `x^2 + (1)/x^2`
Expand the following:
(4a – b + 2c)2
