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inequality with sides of a triangle
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aadil
Riemann Hypothesis
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#1
inequality with sides of a triangle
if a,b,c are the sides of a right triangle prove that c^n > a^n + b^n.n>2
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Last edited by aadil on Mon Nov 09, 2009 6:15 am; edited 1 time in total 
PostPosted: Sun Nov 08, 2009 6:17 am  Back to top 
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x164
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#2
I suppose c is the hypothenuse of the triangle. maybe

Is n>2? For n=1 or n=2 for example your inequality does not hold...

PostPosted: Sun Nov 08, 2009 6:22 am  Back to top 
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hedeng123
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#3
Re: inequality with sides of a triangle
aadil wrote:
if a,b,c are the sides of a right triangle prove that c^n > a^n + b^n



first we have p > 1
(x + y)^p > x^p + y^p

x^p + y^p = (x + y)^p - (x + y)(x + y)^{p - 1} + x^p + y^p = (x + y)^p - x((x + y)^{p - 1} - x^{p - 1}) - y((x + y)^{p - 1} -...

Therefore,

c^n = (c^2)^{\frac {n}{2}} = (a^2 + b^2)^{\frac {n}{2}} > a^n + b^n

while n > 2 and n is positive reals

PostPosted: Sun Nov 08, 2009 6:34 am  Back to top 
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aadil
Riemann Hypothesis
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#4
n>2.sorry i didnt mention before
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PostPosted: Mon Nov 09, 2009 6:15 am  Back to top 
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