$I f x = 1 a n d y = 6 is a solution of the equation 8 x - a y + a^{2} = 0, find the values of a.$

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Solution

$x = 1, y = 6 is a solution of the equation 8 x - a y + a^{2} = 0$

Substituting the value of x and y,

$8 \times 1 - a \times 6 + a^{2} = 0 \Rightarrow 8 - 6 a + a^{2} = 0 \Rightarrow a^{2} - 6 a + 8 = 0 \Rightarrow a^{2} - 2 a - 4 a + 8 = 0 \Rightarrow a (a - 2) - 4 (a - 2) = 0 \Rightarrow (a - 2) (a - 4) = 0 Either a - 2 = 0, then a = 2 O r a - 4 = 0, then a = 4 H e n c e, a = 2, 4$

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