If a-b=3 and a3−b3=117 then find the absolute value of a+b.

Stacie Worsley

Answered question

2021-12-13

If a-b=3 and ${a}^{3}-{b}^{3}=117$ then find the absolute value of a+b.

Answer & Explanation

Joseph Fair

Beginner2021-12-14Added 34 answers

Step 1
Given that a-b=3 and ${a}^{3}-{b}^{3}=117$.
It is known that ${(a-b)}^{3}={a}^{3}-{b}^{3}-3ab(a-b)$.
Given that a-b=3 and ${a}^{3}-{b}^{3}=117$.
${(a-b)}^{3}={a}^{3}-{b}^{3}-3ab(a-b)$ ${3}^{3}=117-3ab\left(3\right)$
27=117-9ab
9ab=90
ab=10
Step 2
${a}^{3}-{b}^{3}=(a-b)({a}^{2}+{b}^{2}+ab)$ $117=3[{(a+b)}^{2}+ab]$ $39={(a+b)}^{2}+10$
a+b=7