Question
Divide $57$ into two parts whose product is $680$.
✓
Answer
Let the one part be $x$.
Then, the other part will be $(57 - x)$.
Thus, we have
$x(57 - x) = 680$
$\Rightarrow 57x - x^2= 680$
$\Rightarrow x^2 - 57x + 680 = 0$
$\Rightarrow x^2 - 17x - 40x + 680 = 0$
$\Rightarrow x(x - 17) - 40(x - 17) = 0$
$\Rightarrow (x - 17)(x - 40) = 0$
$\Rightarrow x - 17 = 0$ or $x - 40 = 0$
$\Rightarrow x = 17$ or $x = 40$
Hence, the two parts are $17$ and $40$.
Then, the other part will be $(57 - x)$.
Thus, we have
$x(57 - x) = 680$
$\Rightarrow 57x - x^2= 680$
$\Rightarrow x^2 - 57x + 680 = 0$
$\Rightarrow x^2 - 17x - 40x + 680 = 0$
$\Rightarrow x(x - 17) - 40(x - 17) = 0$
$\Rightarrow (x - 17)(x - 40) = 0$
$\Rightarrow x - 17 = 0$ or $x - 40 = 0$
$\Rightarrow x = 17$ or $x = 40$
Hence, the two parts are $17$ and $40$.
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