Question

if a,b,c are in continued proportion, show that : a^2+b^2/b(a+c) =b(a+c)/b^2+ c^2​

Answer 1

Step-by-step explanation:

As a, b and c are in continued proportion,

$\small{\frac{a}{b} =\frac{b}{c}}$

= > b² = ac

Solving LHS:

= > (a² + b²)/b(a + c)

= > (a² + ac)/b(a + c)

= > a(a + c)/b(a + c)

= > a/b

Solving RHS:

= > b(a + c)/(b² + c²)

= > b(a + c)/(ac + c²)

= > b(a + c)/c(a + c)

= > b/c

And, from above we know, $\small{\frac{a}{b} =\frac{b}{c}}$

That's how, a^2+b^2/b(a+c) =b(a+c)/b^2+ c^2.

Proved.