Question

1. Укажіть число, що є розв'язком нерівності 3/5 х2 − х − 5/2> 0. ОТВЕТЫ: 0 -1 1 2

Answer 1

$displaystyle tt frac{3}{5}x^2-x-frac{5}{2}>0 : : : : : | cdot 10\displaystyle tt 6x^2-10x-25>0\displaystyle tt 6x^2-10x-25=0\displaystyle tt x=frac{5б5sqrt{7}}{6}$

$displaystyle tt 6(x-frac{5+5sqrt{7}}{6})(x-frac{5-sqrt{7}}{6})>0 : : : : | div6\displaystyle tt (x-frac{5+5sqrt{7}}{6})(x-frac{5-sqrt{7}}{6})>0\1)left { {{displaystyle tt x-frac{5+5sqrt{7}}{6}>0} atop {displaystyle tt x-frac{5-5sqrt{7}}{6}>0}} right. \2)left { {{displaystyle tt x-frac{5+5sqrt{7}}{6}<0} atop {displaystyle tt x-frac{5-5sqrt{7}}{6}<0}} right.$

$1) left { {displaystyle tt {x>frac{5+5sqrt{7}}{6}} atop {displaystyle tt x>frac{5-5sqrt{7}}{6}}} right. \2) left { {{displaystyle tt x<frac{5+5sqrt{7}}{6}} atop {displaystyle tt x<frac{5-5sqrt{7}}{6}}} right. \left { {{{displaystyle tt xin (frac{5+5sqrt{7}}{6};: +infty)} atop {{displaystyle tt xin (-infty;:frac{5-5sqrt{7}}{6})}} right. \\displaystyle tt xin (-infty;: frac{5-5sqrt{7}}{6})cup(frac{5+5sqrt{7}}{6};: +infty)$