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# Algebra

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The expression x^2 + 15x + 54 can be written as (x + a)(x + b), and the expression x^2 - 17x + 72 written as (x - b)(x - c), where a, b, and c are integers. What is the value of a+b+c?

Oct 15, 2022

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What is the value of a+b+c?

Hello Guest!

$$x^2 + 15x + 54=0\\ x=-7.5\pm \sqrt{56.25-54}\\ x\in \{-9,-6\}\\ (x+a)(x+b)=(x+6)(x+9)=0\\ a=6\\ b=9$$

$$x^2 - 17x + 72=0\\ x=8.5\pm \sqrt{72.25-72}\\ x\in \{8,9\} \\ (x-b)(x-c)=(x-9)(x-8)\\ b=9\\ c=8\\ \color{blue}a+b+c=6+9+8=23$$

!

Oct 15, 2022
edited by asinus  Oct 15, 2022