Question

Решите уравнение: 5x^2-3x+6=5(1+√2)^2 -3(1+√2)+6

Answer 1

5x²-3x+6=5(1+√2)²-3(1+√2)+6

5x²-3x+6=5(1+2√2+2)-3-3√2+6

5x²-3x+6=5+10√2+10-3-3√2+6

5x²-3x+6= 18+7√2

5x²-3x-(12+7√2)=0

D= 9+20(12+7√2)= 9+240+140√2= 249+140√2=200+140√2+49= (10√2+7)²

x1= (3+10√2+7)/10= 1+√2

x2= (3-10√2-7)/10= (-4-10√2)/10= (-2-5√2)/5