If 4 (x + y) = 256 and (256) (x - y) = 4, then what is the value of x and y?
17/8, 15/8
Rewrite both sides with base 4 using \(256 = 4^4\).
Step 1 — From \(4^{x+y} = 256 = 4^4\):
\(x + y = 4\)
Step 2 — From \(256^{x-y} = 4 \implies 4^{4(x-y)} = 4^1\):
\(x - y = \tfrac{1}{4}\)
Step 3 — Add and subtract:
\(2x = 4 + \tfrac{1}{4} = \tfrac{17}{4} \implies x = \tfrac{17}{8}\)
\(y = 4 - \tfrac{17}{8} = \tfrac{15}{8}\)
Therefore \((x, y) = \left(\tfrac{17}{8}, \tfrac{15}{8}\right)\).
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