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The sum of two consecutive negative integers whose product is 156. Find the integers

User Sonorx
by
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1 Answer

4 votes

Answer:

The integers are -13 and -12

Explanation:

Let

x ----> the first consecutive negative integer

x+1 ----> the second consecutive negative integer

we know that


x(x+1)=156

Apply the distributive property


x^2+x=156\\x^2+x-156=0

The formula to solve a quadratic equation of the form


ax^(2) +bx+c=0

is equal to


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

in this problem we have


x^2+x-156=0

so


a=1\\b=1\\c=-156

substitute in the formula


x=\frac{-1(+/-)\sqrt{1^(2)-4(1)(-156)}} {2(1)}


x=\frac{-1(+/-)√(625)} {2}


x=\frac{-1(+/-)25} {2}


x_1=\frac{-1(+)25} {2}=12 ----> the solution cannot be a positive number


x_1=\frac{-1(-)25} {2}=-13

therefore


x=-13\\x+1=-12

User Luis Ramirez
by
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