SOLUTION: If a, b, and c are positive integers, find the sum a+b+c if (a^3)(b)=1375, (b^3)(c)=3993 and (a)(c^3)=135.

Algebra ->  Expressions-with-variables -> SOLUTION: If a, b, and c are positive integers, find the sum a+b+c if (a^3)(b)=1375, (b^3)(c)=3993 and (a)(c^3)=135.      Log On


   

Question 1150077: If a, b, and c are positive integers, find the sum a+b+c if (a^3)(b)=1375, (b^3)(c)=3993 and (a)(c^3)=135.
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

HINT. decompose 1375, 3993 and 135 into products of prime numbers.

Then compare indexes in decompositions with the indexes in expressions.

From it, find "a", "b" and "c" through simple logic analysis.

This problem is for advanced students, so if your level is ADEQUATE, you will be able to continue and to complete on your own.

If not, hence you are in wrong class.


I solved here one similar problem under this link

https://www.algebra.com/algebra/homework/Exponents/Exponents.faq.question.1150079.html

https://www.algebra.com/algebra/homework/Exponents/Exponents.faq.question.1150079.html


Consider it as your template to start and to move forward.

You may report me about your progress and/or ask questions.
If you do, then refer to the problem ID number 1150077; otherwise I will not know to whom to answer.

Good luck (!)