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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. 

 Jul 14, 2023
 #1
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-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.

 Jul 14, 2023
 #2
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+3

This is one of the more insidious sh*t answers, they give some "helpful" information then leave you with nothing. B*tch, there is no nice method to solve that third degree polynomial. Do better.

Guest Jul 14, 2023
 #3
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-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}

 Jul 14, 2023
 #4
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I didn't check the imaginary numbers, but the real       

numbers check out right on the money.  Good work.     

.

Bosco  Jul 15, 2023
 #5
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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. 

 Jul 19, 2023

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