Advertisements
Advertisements
Question
If a + b + c = 0, then a3 + b3 + c3 is equal to ______.
Options
0
abc
3abc
2abc
Solution
If a + b + c = 0, then a3 + b3 + c3 is equal to 2abc.
Explanation:
We know that,
a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)
As a + b + c = 0, So, a3 + b3 + c3 – 3abc = (0)(a2 + b2 + c2 – ab – bc – ca) = 0
Hence, a3 + b3 + c3 = 3abc
APPEARS IN
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
104 × 96
Factorise the following using appropriate identity:
9x2 + 6xy + y2
Expand the following, using suitable identity:
(–2x + 3y + 2z)2
Write the following cube in expanded form:
`[x-2/3y]^3`
Factorise the following:
64m3 – 343n3
Simplify: `(a + b + c)^2 - (a - b + c)^2`
If \[x - \frac{1}{x} = 5\] ,find the value of \[x^3 - \frac{1}{x^3}\]
If \[x^2 + \frac{1}{x^2} = 98\] ,find the value of \[x^3 + \frac{1}{x^3}\]
If x = 3 and y = − 1, find the values of the following using in identify:
(9y2 − 4x2) (81y4 +36x2y2 + 16x4)
(a − b)3 + (b − c)3 + (c − a)3 =
\[\frac{( a^2 - b^2 )^3 + ( b^2 - c^2 )^3 + ( c^2 - a^2 )^3}{(a - b )^3 + (b - c )^3 + (c - a )^3} =\]
Evalute : `((2x)/7 - (7y)/4)^2`
If x + y = `7/2 "and xy" =5/2`; find: x - y and x2 - y2
If a + `1/a`= 6 and a ≠ 0 find :
(i) `a - 1/a (ii) a^2 - 1/a^2`
Evaluate: `(2"x"-3/5)(2"x"+3/5)`
Evaluate, using (a + b)(a - b)= a2 - b2.
399 x 401
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`
Which one of the following is a polynomial?
Expand the following:
(–x + 2y – 3z)2
Find the following product:
(x2 – 1)(x4 + x2 + 1)
