Question

if a-b=3 and a^3-b^3=117, then what is a+b

a)5 b)7 c)9 d)11

Answer 1

a-b = 3
a=3+b
${x}^{3} - {y}^{3} = (x - y)( {x}^{2} + {y}^{2} + xy)$
using this formula,

3((3+b^2)+b^2+3b+b^2) = 117
=3(3b^2+3b+3) =117
taking 9 common from both sides,
b^2+b+1=13
b^2+b-12=0
b^2+4b-3b-12=0
b(b+4)-3(b+4)=0
b = 3, -4
if b = 3
a = 6
=a+b = 9
if b = -4
a = -1
a+b = -5
answer is,
9 ..