The Sum Of Two Integers Algebra Problem

Algebra Level 2

The sum of two integers is − 4 -4 . Their product is − 21 -21 . What is the greater integer?


The answer is 3.

Isabelle Barros Rocha by Isabelle Barros Rocha , 20, Brazil

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1 solution

Ellen Sassani
Dec 1, 2017

Let us call our integers a , b ∈ Z \color{#D61F06}{a,b \in \mathbb{Z}} . a b = − 21 , a + b = − 4 \color{#D61F06}{ab = -21, a + b = -4} .

Hence a = − 4 − b \color{#3D99F6}{a = -4 - b} b ( − 4 − b ) = − 21 \color{#3D99F6}{b(-4-b) = -21}

b 2 + 4 b − 21 = 0 \color{#3D99F6}{b^2 + 4b - 21 = 0}

δ = 2 2 + 21 = 5 2 \color{#3D99F6}{\delta = 2^2 + 21 = 5^2}

b = − 2 ± 5 \color{#3D99F6}{b = -2 \pm 5}

Hence, the two integers are − 2 − 5 = − 7 \color{#CEBB00}{-2-5 = -7} and − 2 + 5 = 3 \color{#CEBB00}{-2+5 = 3} .

The greater integer is 3 \color{#CEBB00}{\boxed{3}} .

11 Helpful 0 Interesting 0 Brilliant 0 Confused

idk how you. Just did all that…. but I commend you for doing things the proper way. I just stared at the question until I had an answer and then checked yours to see if I was right.

Sheryl Leelin - 3 years, 6 months ago

This is quite good, but I’m stuck on part of it:

“ b ( − 4 − b ) = − 21 b ( − 4 − b ) = − 21 b(-4-b)=-21b(-4-b)=-21

b 2 + 4 b − 21 = 0 b^2+4b-21=0 ″

Shouldn’t this be

− b 2 − 4 b = − 21 -b^2 - 4b = -21 ?

And shouldn’t it be + 21 +21 on the second line?

The Strategy Gamer - 3 years, 6 months ago

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