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Division of a Polynomial by a Polynomial

If ax + by ...

Question

If $a x + b y = a^{2} - b^{2}$ and $b x + a y = 0,$ find the value of $(x + y)$ .

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Solution

Given,
$a x + b y = a^{2} - b^{2}$ ......(1)

$b x + a y = 0$ .......(2).

Now adding (1) and (2) we get,

$x (a + b) x + (a + b) y = a^{2} - b^{2}$

or, $(a + b) (x + y) = a^{2} - b^{2}$

or, $x + y = a - b$ .

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