Q7 of 53 Page 150

Suppose 3k × b2 = 64 for some positive integers k, b. Find all possible values of k + b.

Given: 3k × b2 = 64


⇒3k × b2 = (2× 3)4


Using For a ≠0 and b ≠ 0, and integer m,


(a × b)m = am × bm


⇒3k × b2 = 24× 34


⇒3k × b2 = 42× 34


On comparing,


k = 4, b = 4


⇒ k+b = 8


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