Advertisements
Advertisements
Question
Find the value of x3 – 8y3 – 36xy – 216, when x = 2y + 6
Advertisements
Solution
Here, we see that, x – 2y – 6 = 0
∴ x3 + (–2y)3 + (–6)3 = 3x(–2y)(–6) ...[Using identity, a + b + c = 0, then a3 + b3 + c3 = 3abc]
⇒ x3 – 8y3 – 216 = 36xy ...(i)
Now, x3 – 8y3 – 36xy – 216
= x3 – 8y3 – 216 – 36xy
= 36xy – 36xy ...[From equation (i)]
= 0
APPEARS IN
RELATED QUESTIONS
Use suitable identity to find the following product:
(x + 8) (x – 10)
Write the following cube in expanded form:
`[3/2x+1]^3`
Evaluate the following using identities:
117 x 83
If `x^2 + 1/x^2 = 66`, find the value of `x - 1/x`
Write in the expanded form:
(2a - 3b - c)2
If a − b = 4 and ab = 21, find the value of a3 −b3
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{x}{y} - \frac{y}{3} \right) \frac{x^2}{16} + \frac{xy}{12} + \frac{y^2}{9}\]
Evaluate:
253 − 753 + 503
If \[x^4 + \frac{1}{x^4} = 623\] then \[x + \frac{1}{x} =\]
Find the square of : 3a - 4b
If a2 - 3a + 1 = 0, and a ≠ 0; find:
- `a + 1/a`
- `a^2 + 1/a^2`
Use the direct method to evaluate the following products :
(8 – b) (3 + b)
Expand the following:
(m + 8) (m - 7)
Expand the following:
`(2"a" + 1/(2"a"))^2`
Find the squares of the following:
(2a + 3b - 4c)
If `x + (1)/x = 3`; find `x^4 + (1)/x^4`
If x + y + z = p and xy + yz + zx = q; find x2 + y2 + z2.
If `"p" + (1)/"p" = 6`; find : `"p"^2 + (1)/"p"^2`
If `"p" + (1)/"p" = 6`; find : `"p"^4 + (1)/"p"^4`
Expand the following:
(3a – 5b – c)2
