If $a + b = 5$ , then the value of $(a - 3)^{7} + (b - 2)^{7}$ is

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Solution

Given $a + b = 5$
$\Rightarrow a = 5 - b$
$(a - 3)^{7} + (b - 2)^{7}$
$= (5 - b - 3)^{7} + (b - 2)^{7}$
$= (2 - b)^{7} + (b - 2)^{7}$
$= (- 1)^{7} (b - 2)^{7} + (b - 2)^{7}$
$= - (b - 2)^{7} + (b - 2)^{7}$
$= 0$
$∴ (a - 3)^{7} + (b - 2)^{7} = 0$ .

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