0\; ,\\\\25x^2-4<0\; \; ,\; \; \; \; (5x-2)(5x+2)<0\; ,\\\\znaki:\; \; +++(-\frac{2}{5})---(\frac{2}{5})+++\\\\x\in (-\frac{2}{5}\; ;\; \frac{2}{5}\; )\; \; \; \Rightarrow \; \; \; x\in (-0,4\, ;\, 0,4\, )" alt="1a)\; \; y=\sqrt{-x^2+3x+4}\; \; \; \Rightarrow \; \; \; -x^2+3x+4\geq 0\; \; ,\\\\x^2-3x-4\leq 0\; \; ,\; \; x_1=-1\; ,\; x_2=4\\\\(x+1)(x-4)\leq 0\\\\znaki:\; \; \; +++[-1\; ]---[\; 4\; ]+++\\\\x\in [-1\, ;\; 4\; ]\\\\1b)\; \; y=\frac{1}{\sqrt{4-25x^2}}\; \; \; \Rightarrow \; \; \; 4-25x^2>0\; ,\\\\25x^2-4<0\; \; ,\; \; \; \; (5x-2)(5x+2)<0\; ,\\\\znaki:\; \; +++(-\frac{2}{5})---(\frac{2}{5})+++\\\\x\in (-\frac{2}{5}\; ;\; \frac{2}{5}\; )\; \; \; \Rightarrow \; \; \; x\in (-0,4\, ;\, 0,4\, )" align="absmiddle" class="latex-formula">
всего 8 целых решений
![b)\; \; 15-x^2+10x\geq 0\; \; \; \Rightarrow \; \; \; x^2-10x-15\leq 0\; ,\\\\D/4=5^2+15=40\; \; ,\\\\x_1=5-\sqrt{40}=5-2\sqrt{10}\approx -1,32\; \; ,\; \; x_2=5+2\sqrt{10}\approx 11,32\; \; ,\\\\x\in [\; 5-2\sqrt{10}\; ;\; 5+2\sqrt{10}\; ]\\\\celue:\; \; x=-1\; ,\; 0\; ,\; 1\; ,\; 2\; ,\; 3\; ,\; 4\; ,\; 5\; ,\; 6\; ,\; 7\; ,\; 8\; ,\; 9\; ,\; 10\; ,\; 11\; .](https://tex.z-dn.net/?f=b%29%5C%3B%20%5C%3B%2015-x%5E2%2B10x%5Cgeq%200%5C%3B%20%5C%3B%20%5C%3B%20%5CRightarrow%20%5C%3B%20%5C%3B%20%5C%3B%20x%5E2-10x-15%5Cleq%200%5C%3B%20%2C%5C%5C%5C%5CD%2F4%3D5%5E2%2B15%3D40%5C%3B%20%5C%3B%20%2C%5C%5C%5C%5Cx_1%3D5-%5Csqrt%7B40%7D%3D5-2%5Csqrt%7B10%7D%5Capprox%20-1%2C32%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20x_2%3D5%2B2%5Csqrt%7B10%7D%5Capprox%2011%2C32%5C%3B%20%5C%3B%20%2C%5C%5C%5C%5Cx%5Cin%20%5B%5C%3B%205-2%5Csqrt%7B10%7D%5C%3B%20%3B%5C%3B%205%2B2%5Csqrt%7B10%7D%5C%3B%20%5D%5C%5C%5C%5Ccelue%3A%5C%3B%20%5C%3B%20x%3D-1%5C%3B%20%2C%5C%3B%200%5C%3B%20%2C%5C%3B%201%5C%3B%20%2C%5C%3B%202%5C%3B%20%2C%5C%3B%203%5C%3B%20%2C%5C%3B%204%5C%3B%20%2C%5C%3B%205%5C%3B%20%2C%5C%3B%206%5C%3B%20%2C%5C%3B%207%5C%3B%20%2C%5C%3B%208%5C%3B%20%2C%5C%3B%209%5C%3B%20%2C%5C%3B%2010%5C%3B%20%2C%5C%3B%2011%5C%3B%20. "b)\; \; 15-x^2+10x\geq 0\; \; \; \Rightarrow \; \; \; x^2-10x-15\leq 0\; ,\\\\D/4=5^2+15=40\; \; ,\\\\x_1=5-\sqrt{40}=5-2\sqrt{10}\approx -1,32\; \; ,\; \; x_2=5+2\sqrt{10}\approx 11,32\; \; ,\\\\x\in [\; 5-2\sqrt{10}\; ;\; 5+2\sqrt{10}\; ]\\\\celue:\; \; x=-1\; ,\; 0\; ,\; 1\; ,\; 2\; ,\; 3\; ,\; 4\; ,\; 5\; ,\; 6\; ,\; 7\; ,\; 8\; ,\; 9\; ,\; 10\; ,\; 11\; .")
всего 13 целых решений
![2)\; \; 3x^2+5x\leq 4\; \; ,\; \; \; 3x^2+5x-4\leq 0\\\\D=73\; ,\; \; x_1=\frac{-5-\sqrt{73}}{6}\approx -2,26\; \; ,\; \; x_2=\frac{-5+\sqrt{73}}{6}\approx 0,59\\\\x\in [\; \frac{-5+\sqrt{73}}{6}\; ;\; \frac{-5+\sqrt{73}}{6}\; ]\\\\naibolshee\; celoe:\; \; x=0\; .](https://tex.z-dn.net/?f=2%29%5C%3B%20%5C%3B%203x%5E2%2B5x%5Cleq%204%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20%5C%3B%203x%5E2%2B5x-4%5Cleq%200%5C%5C%5C%5CD%3D73%5C%3B%20%2C%5C%3B%20%5C%3B%20x_1%3D%5Cfrac%7B-5-%5Csqrt%7B73%7D%7D%7B6%7D%5Capprox%20-2%2C26%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20x_2%3D%5Cfrac%7B-5%2B%5Csqrt%7B73%7D%7D%7B6%7D%5Capprox%200%2C59%5C%5C%5C%5Cx%5Cin%20%5B%5C%3B%20%5Cfrac%7B-5%2B%5Csqrt%7B73%7D%7D%7B6%7D%5C%3B%20%3B%5C%3B%20%5Cfrac%7B-5%2B%5Csqrt%7B73%7D%7D%7B6%7D%5C%3B%20%5D%5C%5C%5C%5Cnaibolshee%5C%3B%20celoe%3A%5C%3B%20%5C%3B%20x%3D0%5C%3B%20. "2)\; \; 3x^2+5x\leq 4\; \; ,\; \; \; 3x^2+5x-4\leq 0\\\\D=73\; ,\; \; x_1=\frac{-5-\sqrt{73}}{6}\approx -2,26\; \; ,\; \; x_2=\frac{-5+\sqrt{73}}{6}\approx 0,59\\\\x\in [\; \frac{-5+\sqrt{73}}{6}\; ;\; \frac{-5+\sqrt{73}}{6}\; ]\\\\naibolshee\; celoe:\; \; x=0\; .")