Решите неравенство методом интервалов:
[tex] \sqrt{x+3} [/tex]* [tex] \sqrt{4x+5} [/tex] < 6

[tex] \sqrt{x+3} * \sqrt{4x+5} \ \textless \ 6[/tex]; _________________________ [tex] \sqrt{(x+3)(4x+5)} \ \textless \ \sqrt{36} [/tex]; _______________________ [tex] (x+3)(4x+5) \ \textless \ 36[/tex]; ________________________________ [tex]4x^2+5x+12x+15-36\ \textless \ 0[/tex]; ____________________________ [tex]4x^2+17x-21\ \textless \ 0[/tex]; _________________________________ [tex]4x^2+17x-21=0; D=17^2-4*4*(-21)=289+336=625=25^2[/tex]; ____________ [tex]x_1= \frac{-17-25}{2*4} =-5,25; x_2= \frac{-17+25}{2*4} =1[/tex]; ___________ _______ + ____________________ - ____________________ + ________ -----------------------------(-5,25)----------------------------------------(1)--------------------------------- x∈(-5,25;1)