Thursday

August 28, 2014

August 28, 2014

Posted by **Mathslover Please help** on Monday, May 6, 2013 at 12:05am.

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**, Monday, May 6, 2013 at 12:14pmhard problem

- Math (algebra) -
**John**, Monday, May 6, 2013 at 7:14pmThe answer is 439

- Math (algebra) -
**Anonymous**, Tuesday, May 7, 2013 at 12:01amwrong ans

- Math (algebra) -
**Mathslover Please help**, Tuesday, May 7, 2013 at 12:11amDude Please Help

- Math (algebra) -
**Athul**, Tuesday, May 7, 2013 at 11:12am775

(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(ab-9)= k^2

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.

- Math (algebra) -
**amgad ahmed**, Tuesday, May 7, 2013 at 11:21am775 is the right answer

- Math (algebra) -
**Mathslover Please help**, Wednesday, May 8, 2013 at 1:50amthanxxxx 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**, Wednesday, May 8, 2013 at 8:07amAthul,can u explain why "implies ab-9=m^2 " can become " using ab=m^2 -9"?

**Related Questions**

Maths - Suppose a and b are positive integers satisfying 1≤a≤31, 1&#...

Math - A smooth partition of the integer n is a set of positive integers a 1 ,a ...

geometry - A smooth partition of the integer n is a set of positive integers a1,...

algebra 1 help please - 4) a student score is 83 and 91 on her first two quizzes...

Math - Find the largest possible degree n≤1000 of a polynomial p(x) such ...

Algebra 2 - Solve. 4a-2≤a+1≤3a+4 4a-2-1≤a+1-1≤3a+4-1 4a-...

plls heeeeeeelp math - How many ordered pairs of positive integers 1≤k&#...

heeeeeeeeelp math - How many ordered pairs of positive integers 1≤k≤...

mathematics - Suppose f(x) is a degree 8 polynomial such that f(2^i)=1/2^i for ...

math - How many ordered pairs of positive integers 1≤k≤n≤50 ...