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if a-b=3 and a 3 -b 3 =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

Grade:9

2 Answers

Nehal Wani
21 Points
13 years ago

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
13 Points
7 years ago
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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