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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.
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