### Math Notes

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#### Algebra Solutions

##### Topics || Problems

Separate 27 into two parts whose product is 92.

This is to find two numbers such that the sum is 27 and the product is 92.

Let $$x + y = 27$$, such that $$xy = 92$$

$$x = 27 - y$$

$$(27 - y) y = 92$$

$$27y - y^2 = 92$$

$$y^2 -27y + 92 = 0$$

$$(y - 23)(y - 4 ) = 0$$

$$y_1 = 4$$ and $$y_2 = 23$$

$$x + 4 = 27$$

$$x = 27 - 4 = 23$$

The numbers are 23 and 4.