KnowledgeBoat Logo
|

Mathematics

Numbers a, b and c are in continued proportion.

Statement 1: (a + b + c)(a - b + c) = a2 + b2 + c2.

Statement 2: b2 = ac and (a + b + c)(a - b + c) = (a + c)2 - b2

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Ratio Proportion

6 Likes

Answer

Both the statements are true.

Reason

Numbers a, b, c are in continued proportion.

Now, (a + b + c)(a - b + c)

= [(a + c) + b][(a + c) - b]

= (a + c)2 - b2

= a2 + c2 + 2ac - b2

Given, a, b and c are in continued proportion,

∴ab=bc⇒b2=ac\therefore \dfrac{a}{b} = \dfrac{b}{c} \\[1em] \Rightarrow b^2 = ac

Substituting the value b2 = ac in above equation,

= a2 + c2 + 2b2 - b2

= a2 + c2 + b2

So, Statement 1 correctly states that: (a + b + c)(a - b + c) = a2 + b2 + c2.

and

Statement 2 correctly states that: b2 = ac

Hence, option 1 is the correct option.

Answered By

1 Like

Related Questions