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About LinkBacksgiven that 0<x<1/2 solve the equation 2x√(1-x^2)+x√(1-4x^2) = 1
September 2nd, 2008, 11:36 PM
given that 0<x<1/2 solve the equation 2x√(1-x^2)+x√(1-4x^2) = 1
square twice.
September 3rd, 2008, 07:08 AM
By Cauchy–Schwarz,Originally Posted by siegfried
given thatsolve the equation
.
We have equality if and only if. Solve that for x.
how do you use cauchy-schwarz
The general Cauchy–Schwarz inequality states that for all,
with equality holding if and only if
and
are linearly dependent in
.
Hence, ifare positive real numbers,
and
.
So, for your problem, if you take,
,
,
) you have
and
:wink:
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