What are the two numbers if the product of two consecutive integers is 72?

Question

What are the two numbers if the product of two consecutive integers is 72?

1 Answer

Impact of this question

33422 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-12-10T18:47:54

We can solve this problem by using $x$ $x$ for one integer and, since they are consecutive numbers, $x + 1$ $x+1$ for the other.

We know that $x \cdot (x + 1) = 72$ $x * (x+1) = 72$ .
This is equivalent to $x^{2} + x = 72$ $x^2 + x = 72$ . After rearranging the equation, we get

$x^{2} + x - 72 = 0$ $x^2 + x - 72 =0$ This is now a tipical quadratic equation $a x^{2} + b x + c = 0$ $ax^2 + bx + c =0$ , for which

$Delta$ = $(b^2 -4ac)$ $->$ $Delta = 1^2 - 4 * 1 *(-72) = 289$

Now, we know that $x_(1,2) = (-b +- sqrt(Delta))/(2a) = (-1 +- sqrt(289))/2$ . Therefore, we have

$x_1 = (-1 -17)/2 = -9$ and $x_2 = (-1 +17)/2 = 8$

So, there are four numbers that satisfy the initiaul equation: for $x=-9$ we have $-9$ and $(-9 + 1) = -8$ , and for $x = 8$ we have $8$ and $(8 + 1) = 9$ .

Therefore, $-9 * (-8) = 72$ and $8 * 9 = 72$ .

Science

Math

Humanities

... and beyond

What are the two numbers if the product of two consecutive integers is 72?

1 Answer

Related questions

Impact of this question