2x^2 - y^2 = 32
2x-y = 8
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2x^2 - ( 2x-8) = 32
y= 2x-8
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Решаем уравнение:
2x^2 - (2x-8) = 32
2x^2 - 2x + 8 - 32 = 0
2x^2 - 2x - 24 = 0 | / 2
x^2 - x - 12 = 0
D = 1 + 4*12 = 49
√49 = 7
x1 = (1+7) / 2 = 8/2 = 4
x2 = (1-7)/2 = -6/2 = -3
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y1 = 2*4 - 8 = 8-8 = 0
y2 = 2*(-3) - 8 = -6 - 8 = -14
Ответ: (4 ; 0 ) и ( -3 ; -14)