If 9x2 + y2 = 37 and xy = 2, x, y > 0, then the value of (27x3 + y3) is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 217
Concept
Basic Algebric identities
(x + y)2 = x2 + y2 + 2xy
(x + y)3 = x3 + y3 + 3x2y + 3xy2
Application
(3x + y)2 = 9x2 + y2 + 6xy
Putting the values of 9x2 + y2 and xy
(3x + y)2 = 37 + 6 × 2
(3x + y)2 = 37 + 12
(3x + y)2 = 49
(3x + y) = 7
(3x + y)3 = 27x3 + y3 + 27x2y + 9xy2
Putting the value of ( 3x + y ) and xy
73 = 27x3 + y3 + 27x2y + 9xy2
343 = 27x3 + y3 + 9xy(3x + y)
343 = 27x3 + y3 + 9 × 2 × 7
27x3 + y3 = 343 – 126
27x3 + y3 = 217