Use the fact:a,b,c real numbers such as a/b + b/c + c/a = 4 and a/c + c/b + b/a = 5
Calcululate a^3/b^3 + b^3/c^3 + c^3/a^3
Hello Mohssine. Those terms will simplify (the subtractions first). Write out the equation Subhotosh provided, replacing x,y,z with a/b, b/c and c/a. You will see cancellations in those subtracted terms and the result will match one of the given values. Continue simplifying. Get a common denominator and combine remaining terms.
You will be substituting 4 and 5 later when you recognize those forms. This will happen after you substitute for x,y,z and start simplifying.how did you explode those two data a/b + b/c + c/a = 4 and a/c + c/b + b/a = 5
No, 5 is correct.a/c + c/b + b/a = 5 this might be equal 3 not 5?
OP stated:Okay, maybe I made a mistake.
So don't go to the corner - you did not make a mistake (that's Jomo's job)a/b + b/c + c/a = 4 and a/c + c/b + b/a = 5
I meant a possible mistake in my own work. (I'm trying to be charitable.)you did not make a mistake
first l made x=a/b; y=b/c; z=c/a; the data become: x+y+z=4; 1/x +1/y + 1/z =5Did you calculate xy & yz & zx?
you ask if i found xy+yz+yx, i did, its 5xyz but i didnt get its valuefirst l made x=a/b; y=b/c; z=c/a; the data become: x+y+z=4; 1/x +1/y + 1/z =5
the second equation gives us: xy+yz+yx=5xyz
i used after that the eq x^3 + y^3 + z^3 - 3xyz = (x + y +z) * (x^2 + y^2 + z^2 - xy - yz - zx) but didnt find the solution yet