If a+b = 5, then the value of (a-3)7 + (b-2)7 is
0
Given: \(a+b = 5\). We need to find \((a-3)^7 + (b-2)^7\). Let's start solving step by step:
- Let \(a-3 = x\) and \(b-2 = y\).
- From \(a+b = 5\), substitute \(a = x+3\) and \(b = y+2\):
- \((x+3) + (y+2) = 5\)
- This simplifies to \(x+y+5 = 5\).
- Thus, \(x+y = 0\).
- The expression becomes \((a-3)^7 + (b-2)^7\), i.e., \(x^7 + y^7\).
- Since \(x+y = 0\), it implies \(y = -x\).
- Now, substitute \(y = -x\) into the expression:
- \(x^7 + (-x)^7 = x^7 - x^7 = 0\).
Therefore, the value of \((a-3)^7 + (b-2)^7\) is \(\boxed{0}\).
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