Try this beautiful problem from Singapore Math Olympiad, 2012, Junior Senior based on Quadratic Equation.

## Quadratic Equation – Singapore Mathematics Olympiad, 2012

Consider the equation

\(\sqrt {3x^2 – 8x + 1} + \sqrt {9x^2 – 24x – 8}\) = 3.

- 9
- 10
- 11
- 12

**Key Concepts**

Quadratic Function

Analysis of Number

Root of Equation

## Check the Answer

But try the problem first…

Answer: 9

Singapore Mathematics Olympiad

Challenges and Thrills – Pre – College Mathematics

## Try with Hints

First hint

As the first hint we can assume :

y =\(3x^2 – 8x + 1 \) then the equation becomes

y + \(\sqrt {3y^2 -11}\) = 3.

Lets try to do the rest of the sum ………………..

Second Hint

If we are still stuck after the first hint we can say :

Then \( \sqrt {3y^2 – 11}\) = 3 – y.

Lets square the both sides , we have \( 3 y^2 – 11 = 9 -6y + y^2 \) ,

Then y = 2 or y = -5

Final Step

Now solve \( 3x^2 – 8x +1 = 2^2 \)

Then x =3 and \(x = – 3^{-1}\)

Hence k = \(\frac {3}{3^{-1}}\) = 9 (Answer )

## Other useful links

- https://www.cheenta.com/area-of-circle-singapore-mathematics-olympiad-2013/
- https://www.youtube.com/watch?v=6Sw-qKpdZTg