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if a+b=c+d and a^2+b^2=c^2+d^2, then sho...

`if a+b=c+d and a^2+b^2=c^2+d^2`, then show by mathematical induction `a^n+b^n=c^n+d^n`

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To prove that if \( a + b = c + d \) and \( a^2 + b^2 = c^2 + d^2 \), then \( a^n + b^n = c^n + d^n \) for all integers \( n \geq 1 \) using mathematical induction, we will follow these steps: ### Step 1: Base Case We start by proving the base case, \( n = 1 \). \[ p(1): a^1 + b^1 = c^1 + d^1 \] ...
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