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

Stacie Worsley 2021-12-13 Answered
If a-b=3 and a3b3=117 then find the absolute value of a+b.
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Expert Answer

Joseph Fair
Answered 2021-12-14 Author has 34 answers
Step 1
Given that a-b=3 and a3b3=117.
It is known that (ab)3=a3b33ab(ab).
Given that a-b=3 and a3b3=117.
(ab)3=a3b33ab(ab)
33=1173ab(3)
27=117-9ab
9ab=90
ab=10
Step 2
a3b3=(ab)(a2+b2+ab)
117=3[(a+b)2+ab]
39=(a+b)2+10
a+b=7
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