If a,b and c are in continued proportion then prove that (ab+bc) is the mean proportional between (a^2+b^2) and (b^2+ c^2)
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Step-by-step explanation:
a, b and c are the continued proportion
a : b = b : c
⇒ a/b = b/c
⇒ b2 = ac
Now a/c = a2 + b2/b2 + c2
⇒ a(b2 + c2) = c(a2 + b2)
L.H.S. = a(b2 + c2) ⇒ a(ac + c2) ⇒ ac(a + c)
R.H.S. = c(a2 + b2) ⇒ c(a2 + ac) ⇒ ac(a + c)
L.H.S. = R.H.S. Hence proved.
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Answer:
lhs
Step-by-step explanation:
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