Advertisements
Advertisements
Question
Find 27a3 + 64b3, if 3a + 4b = 10 and ab = 2
Advertisements
Solution
3a + 4b = 10, ab = 2
(3a + 4b)3 = (3a)3 + 3(3a)2(4b) + 3(3a)(4b)2 + (4b)3
(27a3 + 64b3) = (3a + 4b)3 – 3 (3a)(4b)(3a + 4b)
∵ x3 + y3 = (x + y)3 – 3xy – (x + y)
= 103 – 36ab(10)
= 1000 – 36 × 2 × 10
= 1000 – 720
= 280
APPEARS IN
RELATED QUESTIONS
If a2 + `1/a^2 = 47` and a ≠ 0 find :
- `a + 1/a`
- `a^3 + 1/a^3`
If `a^2 + 1/a^2` = 18; a ≠ 0 find :
(i) `a - 1/a`
(ii) `a^3 - 1/a^3`
If `a + 1/a` = p and a ≠ 0; then show that:
`a^3 + 1/a^3 = p(p^2 - 3)`
The sum of two numbers is 9 and their product is 20. Find the sum of their (i) Squares (ii) Cubes.
If a + 2b + c = 0; then show that a3 + 8b3 + c3 = 6abc
Evaluate the following :
(3.29)3 + (6.71)3
Evaluate the following :
(8.12)3 - (3.12)3
Expand: (3x + 4y)3.
Expand: `[x + 1/y]^3`
(p + q)(p2 – pq + q2) is equal to _____________
