Question
If $x + y = 9, xy = 20$ ; find: $x - y$
✓
Answer
$x + y = 9, xy = 20$
We know $(a + b)$
$= a^2 + 2ab + b^2$
$\therefore (x + y)^2$
$= 81 x^2 + y^2 + 2xy$
$\Rightarrow x^2 + y^2$
$= 81 - 2(120)$
$= 41$
We also know $(a - b)^2$
$= a^2 - 2ab + b^2$
$\Rightarrow (x - y)^2$
$= x^2- 2xy + y^2$
$\Rightarrow (x - y)^2$
$= 41 - 2(20)$
$= 1$
$\Rightarrow x - y$
$= ±1.$
We know $(a + b)$
$= a^2 + 2ab + b^2$
$\therefore (x + y)^2$
$= 81 x^2 + y^2 + 2xy$
$\Rightarrow x^2 + y^2$
$= 81 - 2(120)$
$= 41$
We also know $(a - b)^2$
$= a^2 - 2ab + b^2$
$\Rightarrow (x - y)^2$
$= x^2- 2xy + y^2$
$\Rightarrow (x - y)^2$
$= 41 - 2(20)$
$= 1$
$\Rightarrow x - y$
$= ±1.$
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