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

This is solving quadratic word problems.

User Dcts
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1 Answer

3 votes

Answer:

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

User What Is Sleep
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