Question

решите пожалуйста
$2 sqrt{5 - {x}^{2} } = x - 1$

Answer 1

$2 sqrt{5-x^2} =x-1 \ sqrt{4(5-x^2)} =x-1 \ sqrt{(20-4x^2)} = x-1 \ 20-4x^2=(x-1)^2 \ -4x^2+20=x^2-2x+1 \ -5x^2+2x+19=0 \ 5x^2-2x-19=0 \ D=b^2-4ac = (-2)^2-4*5*(-19)= sqrt{384} = 8 sqrt{6} \ x1= frac{-b+ sqrt{D} }{2a} = frac{2+ 8 sqrt{6} }{10} = frac{1}{5} + frac{4 sqrt{6} }{5} \ x2= frac{-b- sqrt{D} }{2a} = frac{2- 8 sqrt{6} }{10} = frac{1}{5} - frac{4 sqrt{6} }{5}$