How do you find values of a and b, if you are given a+b and ab (and also a^3 + b^3)?

The question I have is: find all the possible solutions of a and b, given a+b=14 and a^3 - b^3 = 81.

Guest Jul 14, 2023

#1**-4 **

a*a*a-b*b*b=81

a=14-b

we substitute-

(14-b)^3-b^3=81

simplify

2744-588b+42b^2-2b^3=81

then just isolate and solve.

Guest Jul 14, 2023

#3**-1 **

a + b=14,

a^3 - b^3 = 81, solve for a, b

Use substitution to get:

**a≈7.27537 and b≈6.72463 {Real solution} a≈6.86232 - 12.1267 i and b≈7.13768 + 12.1267 i {Imag. solution} a≈6.86232 + 12.1267 i and b≈7.13768 - 12.1267 i {Imag. solution}**

Guest Jul 14, 2023

#5**0 **

Yeah, there is no easy answer here, where obviously just taking the cube root is incorrect. If you think that, go back to school and learn the correct answer.

HumenBeing Jul 19, 2023