Q. 253.7( 3 Votes )

If , find the values of a and b.

OR

Factorize: (5a – 7b)3 + (9c – 5a)3 + (7b – 9c)3

Answer :

Given,

Rationalising the above term,



Using the formula (a + b) (a - b) = (a2 – b2)



4 + √15


Comparing with a + √15 b,


a = 4, b = 1


OR


Solution: Given, (5a – 7b)3 + (9c – 5a)3 + (7b – 9c)3


Using the formula, (a + b + c)3 = a3 + b3 + c3 + 3(a + b) (b + c) (c + a)


a3 + b3 + c3 = (a + b + c)3 - 3(a + b) (b + c) (c + a)


(5a 7b)3 + (9c 5a)3 + (7b – 9c)3 = (5a - 7b + 9c – 5a + 7b – 9c)3 – 3(5a – 7b + 9c – 5a) (9c – 5a + 7b – 9c) (7b - 9c + 5a – 7b)


(5a 7b)3 + (9c 5a)3 + (7b 9c)3 = 03 3(-7b + 9c) (-5a + 7b) (-9c + 5a)


(5a – 7b)3 + (9c – 5a)3 + (7b – 9c)3 = 3(5a – 7b) (7b – 9c) (9c – 5a)


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