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.
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.
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}
+184 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.
