Advertisements
Advertisements
Question
If x + 2y = 5, then show that x3 + 8y3 + 30xy = 125.
Sum
Advertisements
Solution
Given x + 2y = 5
(x + 2y)3 = 53
⇒ (x)3 + (2y) + 3(x)(2y)(x + 2y) = 53 ....[Using (a + b)3 = (a)3 + (b)3 + 3ab (a + b)]
⇒ (x)3 + (2y)3 + 6xy(x + 2y) = 125
⇒ (x)3 + (2y)3 + 6xy(5) = 125
⇒ x3 + 8y3 + 30xy = 125.
shaalaa.com
Is there an error in this question or solution?
APPEARS IN
RELATED QUESTIONS
Simplify.
(3r − 2k)3 + (3r + 2k)3
Find the cube of : `2a + 1/(2a)` ( a ≠ 0 )
If `( a + 1/a )^2 = 3 "and a ≠ 0; then show:" a^3 + 1/a^3 = 0`.
Use property to evaluate : 383 + (-26)3 + (-12)3
Expand : (3x - 5y - 2z) (3x - 5y + 2z)
If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^4 + 1/a^4 )`
If 2a - 3b = 10 and ab = 16; find the value of 8a3 - 27b3.
Simplify:
(a + b)3 + (a - b)3
Evaluate the following :
(3.29)3 + (6.71)3
Expand: `[x + 1/y]^3`
