Question

Яку заміну потрібно зробити у рівнянні (×2 -5×)2 - 2(×2 - 5×) - 24 =0 срочноооооо

Answer 1

$\displaystyle\bf\\(x^{2} -5x)^{2} -2(x^{2} -5x)-24=0\\\\x^{2} -5x=m\\\\m^{2} -2m-24=0\\\\D=(-2)^{2} -4\cdot(-24)=4+96=100=10^{2}\\\\\\m_{1} =\frac{2-10}{2} =-4\\\\\\m_{2} =\frac{2+10}{2} =6\\\\\\1)\\\\x^{2} -5x=-4\\\\x^{2} -5x+4=0\\\\D=(-5)^{2} -4\cdot 4=25-16=9=3^{2} \\\\\\x_{1} =\frac{5-3}{2} =1\\\\\\x_{2} =\frac{5+3}{2} =4\\\\2)\\\\x^{2}-5x=6\\\\x^{2} -5x-6=0\\\\D=(-5)^{2} -4\cdot (-6)=25+24=49=7^{2} \\\\\\x_{3} =\frac{5-7}{2} =-1\\\\\\x_{4} =\frac{5+7}{2} =6$

$\displaystyle\bf\\Otvet \ : \ 1 \ ; \ 4 \ ; \ -1 \ ; \ 6$