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Grade: 11

                        

if a,b,c are the positive uneven numbers are in H.P, then show that a2+c2>2b2

3 years ago

Answers : (1)

Arun
24742 Points
							
 

As a,b,c are in HP, we have 2/b = 1/a+1/c.

 

So 4/b2 = 1/a2+1/c2+2/ac -------(1).

 

 

 

Now using AM-GM Inequality

 

a2+c2 > 2ac -----{the equality is removed as a,c cannot be equal as given in the question}

 

1/a2+1/c2 > 2/ac.

 

Now from (1) 4/b2 > 2/ac + 2/ac

 

or 4/b2 > 4/ac, or ac>b2

 

So a2+c2 > 2b2.

3 years ago
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