Advertisements
Advertisements
Question
Find 27a3 + 64b3, if 3a + 4b = 10 and ab = 2
Sum
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
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
Expand.
(7x + 8y)3
Find the cube of : 5a + 3b
Find the cube of : `2a + 1/(2a)` ( a ≠ 0 )
If a + 2b + c = 0; then show that: a3 + 8b3 + c3 = 6abc.
Use property to evaluate:
133 + (–8)3 + (–5)3
If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^4 + 1/a^4 )`
If a + b + c = 0; then show that a3 + b3 + c3 = 3abc.
Simplify:
(a + b)3 + (a - b)3
Simplify:
`("a" + 1/"a")^3 - ("a" - 1/"a")^3`
Expand: `((2m)/n + n/(2m))^3`.
