Question

30 х^2-51х-2=24/х^2-51х (/-дробная черта квадрат икса)

Answer 1

$x^{2}-51x-2=\frac{24}{x^{2}-51x }$

Сделаем замену :

x² - 51x = m , m ≠ 0    ⇒  x ≠ 0    и   x ≠ 51

$m-2=\frac{24}{m}\\\\m-2-\frac{24}{m}=0\\\\m^{2}-2m-24=0\\\\m_{1}=6\\\\m_{2} =-4$

$1)x^{2}-51x=6\\\\x^{2}-51x-6=0\\\\D=(-51)^{2}-4*(-6)=2601+24=2625=(5\sqrt{105} )^{2}\\\\x_{1}=\frac{51-5\sqrt{105} }{2}\\\\x_{2}=\frac{51+5\sqrt{105} }{2}$

$2)x^{2}-51x=-4\\\\x^{2}-51x+4=0\\\\D=(-51)^{2}-4*4=2601-16=2585\\\\x_{3}=\frac{51-\sqrt{2585} }{2}\\\\x_{4} =\frac{51+\sqrt{2585} }{2}$