This is a Test of Mathematics Solution Subjective 83 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
If a and b are positive real numbers such that a + b = 1, prove that +
We replace 1 by a+b and expand the squares.
Now we use A.M. - G.M. inequality to have
Also we apply the square mean inequality to have
Since a+b = 1, we have
Combining all of them we have
Discussion
This is a Test of Mathematics Solution Subjective 83 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
If a and b are positive real numbers such that a + b = 1, prove that +
We replace 1 by a+b and expand the squares.
Now we use A.M. - G.M. inequality to have
Also we apply the square mean inequality to have
Since a+b = 1, we have
Combining all of them we have
Discussion