Questions
Suppose a, b, c are distinct real numbers. If are in A.P. and are in H.P., then
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a
−a2,b,c are in G.P.
b
a + b = c
c
a = b + c
d
a, b, c are in G.P.
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Correct option is A
2b=a+c,b2=2a2c2a2+c2⇒ (a+c)24=2a2c2a2+c2⇒a2+c22+2aca2+c2−8a2c2=0⇒a2+c2+4aca2+c2−2ac=0⇒(a+c)2+2ac(a−c)2=0⇒(a+c)2+2ac=0 [∵ a≠c]⇒4b2+2ac=0⇒−a2,b,c are in G.P.Similar Questions
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