Question

теңсіздік шешу
а) (х+2)*(2-х)<3х^2-8
б) 2х-6<(3-х)*(х+3)

Answer 1

$a)(x+2)(2-x) textless 3x^2-8 \ \ (2+x)(2-x) textless 3x^2-8 \ \ 4-x^2 textless 3x^2-8 \ \ -x^2-3x^2 textless -8-4 \ \ -4x^2 textless -12 \ \ x^2 textgreater 3 \ \ (- infty;- sqrt{3} )U(sqrt{3};+infty) \ \ \ b)2x-6 textless (3-x)(x+3) \ \ 2x-6 textless (3-x)(3+x) \ \ 2x-6 textless 9-x^2 \ \ 2x-6-9+x^2 textless 0 \ \ x^2+2x-15 textless 0 \ \ x_1=-5;x_2=3 \ \ (-5;3)$