Question

12*4^(x^2)-2*4^(x^2+2)+16*4^(x^2-2)=-19*4^(6x+2)

Answer 1

12*4^(x^2)-2*4^(x^2+2)+16*4^(x^2-2)=-19*4^(6x+2)

12*4^(x^2)-2*16*4^(x^2)+16*4^(x^2)/16=-19*4^(6x+2)

12*4^(x^2)-32*4^(x^2)+4^(x^2)=-19*4^(6x+2)

4^(x^2)*(12 - 32 +1) = -19*4^(6x+2)

-19*4^(x^2) = - 19*4^(6x+2)

4^(x^2) = 4^(6x+2)

x^2=6x+2

x^2-6x-2=0

D=36 + 4*2 = 44

x12=(6+-√44)/2 = 3+-√11

сумма = 6

ответ  x=3+√11  x=3-√11 сумма корней = 6