(x^2-2011*x+2010)^1/2+(x^2-2012*x+2011)^1/2=(1997*x-x^2-1996)^1/2

Ответ:

Выражение: (x^2-2011*x+2010)^1//2+(x^2-2012*x+2011)^1//2=(1997*x-x^2-1996)^1//2Шаг 1: x^2//2-2011*x//2+2010//2+(x^2-2012*x+2011)//2-(1997*x-x^2-1996)//2=0Шаг 2: x^2//2-1005.5*x+2010//2+(x^2-2012*x+2011)//2-(1997*x-x^2-1996)//2=0Шаг 3: x^2//2-1005.5*x+1005+(x^2-2012*x+2011)//2-(1997*x-x^2-1996)//2=0Шаг 4: x^2//2-1005.5*x+1005+x^2//2-2012*x//2+2011//2-(1997*x-x^2-1996)//2=0Шаг 5: x^2-1005.5*x+1005-2012*x//2+2011//2-(1997*x-x^2-1996)//2=0Шаг 6: x^2-1005.5*x+1005-1006*x+2011//2-(1997*x-x^2-1996)//2=0Шаг 7: x^2-2011.5*x+1005+2011//2-(1997*x-x^2-1996)//2=0Шаг 8: x^2-2011.5*x+1005+1005.5-(1997*x-x^2-1996)//2=0Шаг 9: x^2-2011.5*x+2010.5-(1997*x-x^2-1996)//2=0Шаг 10: x^2-2011.5*x+2010.5-(1997*x//2-x^2//2-1996//2)=0Шаг 11: x^2-2011.5*x+2010.5-(998.5*x-x^2//2-1996//2)=0Шаг 12: x^2-2011.5*x+2010.5-(998.5*x-x^2//2-998)=0Шаг 13: x^2-2011.5*x+2010.5-998.5*x+x^2//2+998=0Шаг 14: x^2-3010*x+2010.5+x^2//2+998=0Шаг 15: 1.5*x^2-3010*x+2010.5+998=0Шаг 16: 1.5*x^2-3010*x+3008.5=0Ответ: 1.5*x^2-3010*x+3008.5=0Квадратное уравнение - решаем;Находим дискриминант:D=(-3010)^2-4*1.5*3008.5=9060100-4*1.5*3008.5=9060100-6*3008.5=9060100-18051=9042049;x_1=(9042049^0.5-(-3010))/(2*1.5)=(3007-(-3010))/(2*1.5)=(3007+3010)/(2*1.5)=6017/(2*1.5)=6017/3=2005.66666666667x_2=(-9042049^0.5-(-3010))/(2*1.5)=(-3007-(-3010))/(2*1.5)=(-3007+3010)/(2*1.5)=3/(2*1.5)=3/3=1

Источник: https://znanija.com/task/313215