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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