Advertisements
Advertisements
प्रश्न
Without actually calculating the cubes, find the value of the following:
(28)3 + (–15)3 + (–13)3
Advertisements
उत्तर
(28)3 + (–15)3 + (–13)3
Let x = 28, y = −15 and z = −13
It can be observed that,
x + y + z = 28 + (−15) + (−13)
= 28 − 28
= 0
It is known that if x + y + z = 0, then
x3 + y3 + z3 = 3xyz
∴ (28)3 + (–15)3 + (–13)3
= 3(28)(–15)(–13)
= 16380
APPEARS IN
संबंधित प्रश्न
Evaluate the following using suitable identity:
(998)3
Write the expanded form:
`(-3x + y + z)^2`
Find the cube of the following binomials expression :
\[2x + \frac{3}{x}\]
If \[x - \frac{1}{x} = 5\], find the value of \[x^3 - \frac{1}{x^3}\]
If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3
Simplify of the following:
(2x − 5y)3 − (2x + 5y)3
If `x^4 + 1/x^4 = 194, "find" x^3 + 1/x^3`
If a + b = 6 and ab = 20, find the value of a3 − b3
If x + \[\frac{1}{x}\] = then find the value of \[x^2 + \frac{1}{x^2}\].
If \[x - \frac{1}{x} = \frac{1}{2}\],then write the value of \[4 x^2 + \frac{4}{x^2}\]
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
\[\frac{( a^2 - b^2 )^3 + ( b^2 - c^2 )^3 + ( c^2 - a^2 )^3}{(a - b )^3 + (b - c )^3 + (c - a )^3} =\]
If a2 - 5a - 1 = 0 and a ≠ 0 ; find:
- `a - 1/a`
- `a + 1/a`
- `a^2 - 1/a^2`
Evaluate: 20.8 × 19.2
Simplify by using formula :
(x + y - 3) (x + y + 3)
Simplify by using formula :
(1 + a) (1 - a) (1 + a2)
If x + y + z = 12 and xy + yz + zx = 27; find x2 + y2 + z2.
If `"p" + (1)/"p" = 6`; find : `"p"^4 + (1)/"p"^4`
Simplify:
`("a" - 1/"a")^2 + ("a" + 1/"a")^2`
Using suitable identity, evaluate the following:
101 × 102
