If 2a+3b=5 and ab=3 then find 8a3-27b3
Hi!
If the question is “ If 2a+3b=5 and ab=3 then find 8a3+27b3”, then the answer is given as,
Given, 2a + 3b = 5 and ab = 3
2a + 3b = 5
Cubing on both sides, we get
(2a + 3b)3 = (5)3 = 125
⇒(2a)3 + (3b)3 + 2 × 2a × 3b (2a + 3b) = 125
⇒ 8a3 + 27b3 + 12ab (2a + 3b) = 125
⇒ 8a3 + 27b3 + 12 × 3 (5) = 125 (2a + 3b = 5 and ab = 3)
⇒ 8a3 + 27b3 + 180 = 125
⇒8a3 + 27b3 = 125 – 180 = –55
Thus, the value of 8a3 + 27b3 is –55.
Cheers!