Find relation between a and b:
$(2 a - b)^{2} + 2 (2 a - b) - 8 = 0$

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Solution

Let $2 a - b = x$
So the equation is $x^{2} + 2 x - 8 = 0 x^{2} + 4 x - 2 x - 8 = 0 x (x + 4) - 2 (x + 4) = 0 (x - 2) (x + 4) = 0 x = 2, - 4$
So, $2 a - b = 2; 2 a - b = - 4 2 a = b + 2; 2 a = b - 4$

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