If (4a+3b)=10 and ab = 2 find the value of (64a^3 + 27b^3) 

Asked by sayantikasingh3318.9sdatl | 17th Aug, 2020, 09:39: PM

Expert Answer:

Given: (4a + 3b) = 10 and ab = 2
(64a3 + 27b3) = (4a)3 + (3b)3
As we know that x3 + y3 = (x + y) (x2 - xy + y2), so we have
 
(4a)3 + (3b)3 
= (4a + 3b)(16a2 - 12ab + 9b2)
= 10(16a2 - 12x2 + 9b2)
= 10[(16a2 + 9b2) - 24]
= 10[(4a)2 + (3b)2] - 240
= 10[(4a + 3b)2 - 2(4a)(3b)] - 240
= 10[102 - 24x2] - 240
= 10(100 - 48) - 240
= 10 x 52 - 240
= 520 - 240
= 280

Answered by Renu Varma | 18th Aug, 2020, 11:31: AM