Posted by Anonymous on Thursday, February 14, 2013 at 12:43pm.
If a, b and c are sides of a triangle
Then prove that 1≤ [(a^2+b^2+c^2)/(ab + bc+ca)]

maths  Steve, Thursday, February 14, 2013 at 4:26pm
so, we want to show that
ab+bc+ca <= (a^2+b^2+c^2)
since all squares are positive,
0 <= (ab)^2 + (ac)^2 + (bc)^2
0 <= a^22ab+b^2 + a^22ac+c^2 + b^22bc+c^2
0 <= 2(a^2+b^2+c^2)  2(ab+ac+bc)
ab+ac+bc <= a^2+b^2+c^2
This is in fact true for any three real numbers, not just sides of a triangle
Answer This Question
Related Questions
 Maths  Prove that the triangle formed by the points of contact of the sides of ...
 Maths(help me plz..!  The sides of a triangle are of lenths x*y*, x*+y* and ...
 MATH Calculus Homework PLEASE HELP!  Let T be the triangle 1≤x≤2, 0...
 algebra 1 help please  4) a student score is 83 and 91 on her first two quizzes...
 Maths  ABC is an isosceles triangle in which the equal sides are AB and A.If AD...
 Maths  X and Y are points on the sides BC and AC of a triangle ABC respectively...
 Maths  Prove that any two sides of a triangle are together greater than twice ...
 Maths  Let f be a function such that f(−6)=−6, f(6)=6, f is ...
 PRE  CALCULUS  Eliminate the parameter t. Find a rectangular equation for the ...
 bctc  Suppose that 3 ≤ f '(x) ≤ 5 for all values of x. prove that ...
More Related Questions