Questions
Suppose are positive real numbers. If are in A.P. and are in H.P., then
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a
a=b=c
b
2b=3a+c
c
b2=ac/8
d
none of these
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Correct option is A
We have 2b=a+c and b2=2a2c2a2+c2∴ a+c22=2a2c2a2+c2⇒(a+c)2a2+c2=8a2c2⇒ a2+c22+2aca2+c2−8a2c2=0⇒ a2+c2+4aca2+c2−2ac=0⇒ (a+c)2+2ac(a−c)2=0⇒ a−c=0 or (a+c)2+2ac=0As (a+c)2+2ac>0, we get a=c⇒a=b=cSimilar Questions
Given that
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