Question

Найдите область определения функции y=(5x^3 -2x)/√x^2 -11x+28

Answer 1

$y= \frac{5 x^{3}-2x }{ \sqrt{ x^{2} -11x+28} } \left \{ {{ x^{2} -11x+28 \geq 0} \atop { x^{2} -11x+28 \neq 0}} \right. =\ \textgreater \ x^{2} -11x+28\ \textgreater \ 0$
метод интервалов:
1.  x²-11x+28=0.
a=1, b=-11, c=28
D=(-11)²-4*1*28=121-112=9
$x_{1,2} = \frac{-(-11)+- \sqrt{9} }{2*1} = \frac{11+-3}{2}$
x₁=4, x₂=7

2. +++++(4)-----(7)+++++++>x

3. x∈(-∞;4)∪(7;∞)