posted by Mathslover Please help .
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.
The answer is 439
Dude Please Help
implies ab-9=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 b-a =6 using ab=m^2 -9
therefore max of b=31 then a = 25 therefore ab= 775 which is 9 less than 28^2.
775 is the right answer
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.
Athul,can u explain why "implies ab-9=m^2 " can become " using ab=m^2 -9"?