![(x^2+6x+11)(x^2+6x+13)\leq 8\\\\t=x^2+6x+11\; \; \Rightarrow \; \; t\cdot (t+2)\leq 8\; \; ,\; \; t^2+2t-8\leq 0\; ,\\\\t_1=-4\; ,\; \; t_2=2\; \; (teorema\; Vieta)\\\\(t+4)(t-2)\leq 0\; ,\; \; \; +++[-4\, ]---[\, 2\, ]+++\\\\t\in [-4,2]\; \; \; \; ili\; \; \; \; -4\leq t\leq 2\\\\-4\leq x^2+6x+11\leq 2\; \; \Rightarrow \; \; \left \{ {{x^2+6x+11\leq 2} \atop {x^2+6x+11\geq -4}} \right. \; \left \{ {{x^2+6x+9\leq 0} \atop {x^2+6x+15\geq 0}} \right. \; \left \{ {{(x+3)^2\leq 0} \atop {x^2+6x+15\geq 0}} \right.](https://tex.z-dn.net/?f=%28x%5E2%2B6x%2B11%29%28x%5E2%2B6x%2B13%29%5Cleq%208%5C%5C%5C%5Ct%3Dx%5E2%2B6x%2B11%5C%3B%20%5C%3B%20%5CRightarrow%20%5C%3B%20%5C%3B%20t%5Ccdot%20%28t%2B2%29%5Cleq%208%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20t%5E2%2B2t-8%5Cleq%200%5C%3B%20%2C%5C%5C%5C%5Ct_1%3D-4%5C%3B%20%2C%5C%3B%20%5C%3B%20t_2%3D2%5C%3B%20%5C%3B%20%28teorema%5C%3B%20Vieta%29%5C%5C%5C%5C%28t%2B4%29%28t-2%29%5Cleq%200%5C%3B%20%2C%5C%3B%20%5C%3B%20%5C%3B%20%2B%2B%2B%5B-4%5C%2C%20%5D---%5B%5C%2C%202%5C%2C%20%5D%2B%2B%2B%5C%5C%5C%5Ct%5Cin%20%5B-4%2C2%5D%5C%3B%20%5C%3B%20%5C%3B%20%5C%3B%20ili%5C%3B%20%5C%3B%20%5C%3B%20%5C%3B%20-4%5Cleq%20t%5Cleq%202%5C%5C%5C%5C-4%5Cleq%20x%5E2%2B6x%2B11%5Cleq%202%5C%3B%20%5C%3B%20%5CRightarrow%20%5C%3B%20%5C%3B%20%5Cleft%20%5C%7B%20%7B%7Bx%5E2%2B6x%2B11%5Cleq%202%7D%20%5Catop%20%7Bx%5E2%2B6x%2B11%5Cgeq%20-4%7D%7D%20%5Cright.%20%5C%3B%20%5Cleft%20%5C%7B%20%7B%7Bx%5E2%2B6x%2B9%5Cleq%200%7D%20%5Catop%20%7Bx%5E2%2B6x%2B15%5Cgeq%200%7D%7D%20%5Cright.%20%5C%3B%20%5Cleft%20%5C%7B%20%7B%7B%28x%2B3%29%5E2%5Cleq%200%7D%20%5Catop%20%7Bx%5E2%2B6x%2B15%5Cgeq%200%7D%7D%20%5Cright. "(x^2+6x+11)(x^2+6x+13)\leq 8\\\\t=x^2+6x+11\; \; \Rightarrow \; \; t\cdot (t+2)\leq 8\; \; ,\; \; t^2+2t-8\leq 0\; ,\\\\t_1=-4\; ,\; \; t_2=2\; \; (teorema\; Vieta)\\\\(t+4)(t-2)\leq 0\; ,\; \; \; +++[-4\, ]---[\, 2\, ]+++\\\\t\in [-4,2]\; \; \; \; ili\; \; \; \; -4\leq t\leq 2\\\\-4\leq x^2+6x+11\leq 2\; \; \Rightarrow \; \; \left \{ {{x^2+6x+11\leq 2} \atop {x^2+6x+11\geq -4}} \right. \; \left \{ {{x^2+6x+9\leq 0} \atop {x^2+6x+15\geq 0}} \right. \; \left \{ {{(x+3)^2\leq 0} \atop {x^2+6x+15\geq 0}} \right.")
0.\\\\\left \{ {{x=-3} \atop {x^2+6x+15>0}} \right. \; \; \Rightarrow \; \; \underline {x=-3}" alt="a)\; \; (x+3)^2\leq 0\; \; \Rightarrow \; \; (x+3)^2=0\; ,\; \; x+3=0\; ,\; \; x=-3\; .\\\\b)\; \; x^2+6x+15\geq 0\; ,\; \; D/4=9-15=-12<0\; \; \Rightarrow \; \; x^2+6x+15>0.\\\\\left \{ {{x=-3} \atop {x^2+6x+15>0}} \right. \; \; \Rightarrow \; \; \underline {x=-3}" align="absmiddle" class="latex-formula">