Maximum Solution

Algebra Level 1

x x and y y are numbers that satisfy the equations y = x y = x and y = x 2 − 13 x + 33 y = x^2 - 13 x + 33 . What is the largest possible value of x x ?


The answer is 11.

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Arron Kau by Arron Kau

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1 solution

Arron Kau Staff
May 13, 2014

Substituting the first equation into the second, we have x = x 2 − 13 x + 33 0 = x 2 − 14 x + 33 = ( x − 3 ) ( x − 11 ) . \begin{aligned} x &= x^2 - 13 x + 33 \\ 0 &= x^2 - 14x + 33 \\ &= (x-3)(x-11). \\ \end{aligned}

This has solutions x = 3 , 11 x = 3, 11 . Thus x = 11 x = 11 is the largest possible value of x x .

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