Question

If a, b, c are in continued proportion,
show that:
a²+b²/b(a+c) =b(a+c) /b²+c²
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Answer 1

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.

Answer 2

Step-by-step explanation:

Given,

a,b,c are in continued proportion.

We know that,

If a,b,c are in continued proportion, then

⇒ (a/b) = (b/c)

⇒ b² = ac     ------ (1)

Given,

(a² + b²)/b(a + c) = b(a + c)/(b² + c²)

⇒ (a² + b²)(b² + c²) = b²(a + c)(a + c)

⇒ (a² + ac)(ac + c²) = ac(a + c)²

⇒ ac(a + c)(a + c) = ac(a + c)²

⇒ ac(a + c)² = ac(a + c)²

∴ LHS = RHS

Hope it helps!