# Quadratic Equation | SMO, 2012 | Junior Section

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

Consider the equation

$\sqrt {3x^2 - 8x + 1} + \sqrt {9x^2 - 24x - 8}$ = 3.

• 9
• 10
• 11
• 12

### Key Concepts

Analysis of Number

Root of Equation

Challenges and Thrills - Pre - College Mathematics

## Try with Hints

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 ....................

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

Now solve $3x^2 - 8x +1 = 2^2$

Then x =3 and $x = - 3^{-1}$

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

## Subscribe to Cheenta at Youtube

This site uses Akismet to reduce spam. Learn how your comment data is processed.

### Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.