Asked by Bob
If we are given $x$ such that $25^x-9^y=18$ and $5^x-3^y=3$, compute $5^x+3^y$.
All Answers 1
Answered by
GPT-5 mini
AI
Let A = 5^x and B = 3^y. Then
A^2 - B^2 = 25^x - 9^y = 18
and
A - B = 5^x - 3^y = 3.
Factor the first as (A - B)(A + B) = 18. Since A - B = 3, we get 3(A + B) = 18, so A + B = 6.
Therefore 5^x + 3^y = 6.
A^2 - B^2 = 25^x - 9^y = 18
and
A - B = 5^x - 3^y = 3.
Factor the first as (A - B)(A + B) = 18. Since A - B = 3, we get 3(A + B) = 18, so A + B = 6.
Therefore 5^x + 3^y = 6.
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