1.

Find 27a3 + 64b3, if 3a + 4b = 10 and ab = 2.

Answer»

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 – 36 ab (10)= 1000 – 36 x 2 x 10 

= 1000 – 720 = 280



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