Infinite Roots

Algebra Level 2

If the following equation has infinite number of roots, what is the sum of the constants a + b a+b : 3 a x + 11 ⋅ 9 − 5 x + 11 = 2 7 x + b ? 3^{ax+11} \cdot 9^{-5x+11}=27^{x+b}?

20 22 18 24

Ajay Dutta by Ajay Dutta , 24, India

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1 solution

Harish Chauhan
Mar 26, 2014

Make the base equal to 3 on both sides, you will get

3^((a-10)x+33)=3^(3x+3b)

then divide by 3^(3x+3b) on both sides gives 3^((a-13)x+(33-3b))=1

So to equate both side we must have a=13; 33-3b=0 or b =11

Thus a+b=24.

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