Решите уравнение: (2x²+3)² - 12(2x² + 3) + 11 = 0

( 2x^2 + 3 )^2 - 12( 2x^2 + 3 ) + 11 = 0 2x^2 + 3 = a a^2 - 12a + 11 = 0 D = 144 - 44 = 100 = 10^2 a1 = ( 12 + 10 ) : 2 = 11 a2 = ( 12 - 10 ) : 2 = 1 1) 2x^2 + 3 = 112x^2 = 8 X^2 = 4 X1,2 = ( + ; - ) 2 2) 2x^2 + 3 = 1 2x^2 = - 2 х^2 = - 1 Нет решений Ответ 2 ; - 2

[latex](2x^2+3)^2-12(2x^2+3)+11=0\ m=2x^2+3 extgreater 0\ m^2-12m+11=0\ Delta =144-44=100 extgreater 0\ m_1= frac{12-10}{2}= frac{2}{2}=1\ m_2= frac{12+10}{2}=11\ 2x^2+3=1iff2x^2=-2\ 2x^2+3=11iff 2x^2=8iff x^2=4\ x^2-4=(x-2)(x+2)=0iff x-2=0; x+2=0\ x_1=-2;x_2=2 [/latex]