Quadratic Equation | SMO, 2012 | Junior Section

Consider the equation

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

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 )

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