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The product of two consecutive numbers is 72. Use a quadratic equation to find the two sets of numbers.

User Gabhijit
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1 Answer

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Given:

The product of two consecutive numbers is 72.

To find:

The two numbers by using the quadratic equation.

Solution:

Let the two consecutive numbers are x and (x+1).

The product of two consecutive numbers is 72.


x(x+1)=72


x^2+x-72=0

Splitting the middle term, we get


x^2+9x-8x-72=0


x(x+9)-8(x+9)=0


(x+9)(x-8)=0

Using zero product property, we get


x+9=0 and
x-8=0


x=-9 and
x=8

If
x=-9, then


x+1=-9+1


x+1=-8

If
x=8, then


x+1=8+1


x+1=9

Therefore, the two consecutive numbers are either 8,9 or -9,-8.

User Glauco Cucchiar
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