Question

If a³+b³=341 and ab=30 then , find the value of a+b

Answer 1

ab = 30

a = 30/b

a^3 + b^3 = 341

( 30 / b )^3 + b^3 = 341

27000 / b^3 + b^3 = 341

b^6 - 341b^3 + 27000 = 0

b^6 - 125b^3 - 216b^3 + 27000 = 0

b^3 ( b^3 - 125 ) - 216 ( b^3 - 125 ) = 0

( b^3 - 125 ) ( b^3 - 216 ) = 0

b^3 - 125 = 0. or b^3 - 216 = 0

b^3 = 125. or. b^3 = 216

b = 5. or. b = 6.

similarly

a = 6. or a = 5

a + b = 6 + 5 = 11

or

a + b = 5 + 6 = 11

Answer 2

( a+b)^3 = a^3 + b^3 + 3 ab (a+b)
(a+b)^3 = 341 + 3 (30) (a+b)
(a+b)^3/(a+b)= 341+90
(a+b)^2 = 441
(a+b)=_/441
a+b=21