Posted by Mathslover Please help on .
Suppose a and b are positive integers satisfying 1≤a≤31, 1≤b≤31 such that the polynomial P(x)=x^3−ax^2+a^2b^3x+9a^2b^2 has roots r, s, and t.
Given that there exists a positive integer k such that (r+s)(s+t)(r+t)=k^2, compute the maximum possible value of ab.

Math (algebra) 
hans,
hard problem

Math (algebra) 
John,
The answer is 439

Math (algebra) 
Anonymous,
wrong ans

Math (algebra) 
Mathslover Please help,
Dude Please Help

Math (algebra) 
Athul,
775
(r+s)(s+t)(r+t)= (r+s+t)(rs+sr+st)rst
=a(a^2.b^3) (9ab)=k^2
implies
a^2.b^2(ab9)= k^2
implies ab9=m^2 where m is an integer as k^2 is a perfect square
given max value of a and b can be 31 and without loss of generality we take a<b, then we find ba =6 using ab=m^2 9
therefore max of b=31 then a = 25 therefore ab= 775 which is 9 less than 28^2. 
Math (algebra) 
amgad ahmed,
775 is the right answer

Math (algebra) 
Mathslover Please help,
thanxxxx Sir . Can yiu please do this question also
Find the sum of squares of all real roots of the polynomial f(x)=x^5−7x^3+2x^2−30x+6. 
Math (algebra) 
hans,
Athul,can u explain why "implies ab9=m^2 " can become " using ab=m^2 9"?