Question

The product of two consecutive odd integers is equal to 30 more than the first. Find the integers.

This is solving quadratic word problems.

Answer 1

The integers are

5 and 7

Explanation:

Let

x ---> the first consecutive odd integer

x+2 ---> the second consecutive odd integer

we know that

The algebraic expression that represent this situation is

`x(x+2)=x+30`

solve for x

`x^2+2x=x+30\\x^2+2x-x-30=0\\x^2+x-30=0`

Solve the quadratic equation

The formula to solve a quadratic equation of the form

`ax^(2) +bx+c=0`

is equal to

`x=\frac{-b\pm\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`x^(2) +x-30=0`

so

`a=1\\b=1\\c=-30`

substitute in the formula

`x=\frac{-1\pm\sqrt{1^(2)-4(1)(-30)}} {2(1)}`

`x=\frac{-1\pm√(121)} {2}`

`x=\frac{-1\pm11} {2}`

`x=\frac{-1+11} {2}=5`

`x=\frac{-1-11} {2}=-6` ---> is not a odd integer

For x=5

The numbers are

`x=5\\x+2=7`

so

5 and 7