Grade 9Algebra
if a-b=3 and a3 -b3=117 ,then what is the value of a+b
if a-b=3 and a3 -b3=117 ,then what is the value of a+b
2 Answers
Nehal Wani
a-b=3
Cubing both sides, we get:
a3-b3-3ab(a-b)=27
117-3ab(3)=27
-9ab=-90
ab=10
a3-b3=(a-b)(a2+b2+ab)
117=3[(a+b)2+ab]
39=(a+b)2+10
(a+b)2=40
a+b=±7
annabeth
a3-b3=(a-b)(a2+ab+b2)
a-b=3
a3-b3=117
117=(3)[(a-b)2+3ab]
117=(3)[(3)2+3ab]
39=9+3ab
30=3ab
10=ab
(a+b)2=(a-b)2+4ab
(a+b)2=(3)2+40
(a+b)2=49
taking sqaure root on both sides
a+b=49
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