SOLUTION: IF a+b=1,a>0,b>0,then show 1/a+1/b>=4

Algebra ->  Proportions  -> Lessons -> SOLUTION: IF a+b=1,a>0,b>0,then show 1/a+1/b>=4      Log On


   

Question 44593: IF a+b=1,a>0,b>0,then show 1/a+1/b>=4
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
IF a+b=1,a>0,b>0,then show 1/a+1/b>=4
1/A + 1/B = (A+B)/AB
TST (A+B)/AB>=4
SINCE A>0 AND B>0 ,AB>0..SO WE CAN MULTIPLY BOTH SIDES WITH AB
TST A+B>=4AB
TST A+B-4AB>=0
A+B=1
B=1-A
A+B-4AB=1-4A(1-A)=1-4A+4A^2=(2A-1)^2..THIS BEING A PERFECT SQUARE IS ALWAYS >=0...
PROVED