Question

Срооочно! Плачу 40 баллов! (х²- х - 1 )² - 10(х² - х - 1) + 9 = 0 Через дискриминант и замену!

Answer 1

Производим замену: х^2-х-1= у
${y}^{2} - 10y + 9 = 0 \\ d = 100 - 36 = 64 \\ y1 = \frac{10 - 8}{2} = 1 \\ y2 = \frac{10 + 8}{2} = 9 \\ {x}^{2} - x - 1 = 1 \\ {x }^{2} - x - 2 = 0 \\ x1 = 2 \\ x2 = - 1 \\ {x}^{2} - x - 1 = 9 \\ {x}^{2} - x - 10 = 0 \\ x3 = \frac{1 - \sqrt{41} }{2} \\ x4 = \frac{1 + \sqrt{41} }{2}$