The product of two consecutive integers is 482 more than the next integer. What is the largest of the three integers?

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Answer 1 · 2017-02-15T12:53:56

The largest is 24 or -20.
Both solutions are valid.

Let the three numbers be $x, x + 1 and x + 2$ $x, x+1 and x+2$

The product of the first two differs from the third by 482.

$x \times (x + 1) - (x + 2) = 482$ $x xx (x+1) - (x+2) = 482$

$x^{2} + x - x - 2 = 482$ $x^2+x -x -2 = 482$

$x^{2} = 484$ $x^2 = 484$

$x = \pm \sqrt{484}$ $x = +-sqrt484$

$x = \pm 22$ $x = +-22$

Check: $22 \times 23 - 24 = 482$ $22 xx 23 - 24 = 482$

$- 22 \times - 21 - (- 20) = 482$ $-22 xx -21 - (-20) = 482$

Both solutions are valid.