Question

Find the third proportional to a/b+b/a and a/b

Answer 1

Step-by-step explanation:

Let’s take the third proportional to a – b and a

2

–b

2

be x

So, a–b,a

2

–b

2

, x are in continued proportion

$$a – b: a^2 – b^2 = a^2 – b^2: x$$

a

2

−b

2

a−b

=

x

a

2

−b

2

x=

a−b

(a

2

−b

2

)

2

x=

a−b

(a+b)(a−b)(a

2

−b

2

)

x=(a+b)(a

2

−b

2

)