SOLUTION: if x<1, prove that (1+x)^1+x(1-x)^1-x > 1

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Question 71407:
if x<1, prove that (1+x)^1+x(1-x)^1-x > 1
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
if x<1, prove that (1+x)^1+x(1-x)^1-x > 1
HAVE YOU TYPED PROPERLY?AS YOU TYPED IT BECOMES
TST
1+X+X-X^2-X>1
LHS = 1+X-X^2 =1-[X^2-2X*0.5+0.5^2]+0.5^2
=1.25-(X-0.5)^2<=1.25 SINCE (X-0.5)^2>=0
IF X<1,X-0.5<0.5....HENCE (X-0.5)^2<0.25
LHS<=1.25-0.25=1
SO PLEASE CHECK YOUR PROBLEM