Advertisements
Advertisements
प्रश्न
If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.
Advertisements
उत्तर
Since, x + y + z = 0
= x + y = −z(x + y)3 = (−z)3
= x3 + y3 + 3xy(x + y) = (−z)3
= x3 + y3 + 3xy(−z) = −z3 ...[∵ x + y = −z]
= x3 + y3 − 3xyz = (−z)3
= x3 + y3 + z3 = 3xyz
Hence, if x + y + z = 0, then
x3 + y3 + z3 = 3xyz
APPEARS IN
संबंधित प्रश्न
Verify:
x3 + y3 = (x + y) (x2 – xy + y2)
Simplify the following products:
`(2x^4 - 4x^2 + 1)(2x^4 - 4x^2 - 1)`
Write in the expanded form:
`(m + 2n - 5p)^2`
If a2 + b2 + c2 = 16 and ab + bc + ca = 10, find the value of a + b + c.
Find the following product:
\[\left( \frac{x}{2} + 2y \right) \left( \frac{x^2}{4} - xy + 4 y^2 \right)\]
Find the following product:
If a + b = 8 and ab = 6, find the value of a3 + b3
(a − b)3 + (b − c)3 + (c − a)3 =
If a + b + c = 0, then \[\frac{a^2}{bc} + \frac{b^2}{ca} + \frac{c^2}{ab} =\]
If a + b + c = 9 and ab + bc + ca =23, then a3 + b3 + c3 − 3abc =
The product (x2−1) (x4 + x2 + 1) is equal to
Evaluate `(a/[2b] + [2b]/a )^2 - ( a/[2b] - [2b]/a)^2 - 4`.
If a + b = 7 and ab = 10; find a - b.
Use the direct method to evaluate :
(0.5−2a) (0.5+2a)
Evaluate: (1.6x + 0.7y) (1.6x − 0.7y)
If `"a" + 1/"a" = 6;`find `"a" - 1/"a"`
If `"a" - 1/"a" = 10;` find `"a" + 1/"a"`
If `x + (1)/x = "p", x - (1)/x = "q"`; find the relation between p and q.
Simplify:
(2x + y)(4x2 - 2xy + y2)
Expand the following:
`(4 - 1/(3x))^3`
