Question

найти сумму корней $x^{2} +6+ frac{2}{ x^{2} -9} =5x- frac{4}{18-2 x^{2} }$

Answer 1

$x^2 + 6 + frac{2}{x^2-9} = 5x - frac{4}{18-2x^2}$

$frac{x^4 - 3x^2 - 52}{x^2-9} = frac{5x^3 - 45x + 2}{x^2-9}$

$x^4 - 3x^2 - 52 = 5x^3 - 45x + 2$

$x^4 - 5x^3 - 3x^2 + 45x - 54 = 0$

$(x-3)^2(x-2)(x+3) = 0$

$(x-3)^2 = 0 ; x - 2 = 0; x + 3 = 0$

$x = 3 ; x = 2 ; x = -3$

$x = 2$