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Question

If a , b , c are in H . P . show that
ad > bc

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Solution

a , b , c , d are in H . P .
b is the H . M of a ,and c are there A . M is a+b2 and G . M is ac
c is the H . m of b and d are their A . M is b+d2 and G . M is bd
Also the A > G > M where A , G , H are respectively means
a+c2>bandb+d2>cA>H
Add ,a+c2+b+d2>B+cora+b+c+d>2ab+2cOra+b>b+c. Thisis(b)ac>bandbd>cG>H
Multipy Acbd>bcoracbd>b2c2orad>bc This is (a)

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