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schepotkina [342]
3 years ago
12

Find two consecutive even integers such that the square of the second, decreased by twice the first is 52

Mathematics
1 answer:
Fiesta28 [93]3 years ago
8 0

Let the first integer be x. So, the next even number is x+2

Let's translate the formula: the square of the second is (x+2)^2, twice the first is 2x. So, the equation is

(x+2)^2 - 2x = 52

Expand the square to get

x^2+4x+4-2x = 52 \iff x^2+2x+4 = 52 \iff x^2+2x - 48 = 0

The solutions to this equations are

x = -8,\quad x = 6

So, the possible consecutive even numbers are

-8\text{ and } -6\quad\text{or}\quad 6\text{ and } 8

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