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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

But try the problem first…

Source

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 )