E:7042
E:7042 (Mariș Ilieș)
Fie Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F = \frac{x^4 - 10x^3 + 35x^2 - 50x +24}{x^3 - 9x^2 + 26x - 24}} . Să se determine Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x \in \mathbb{R}} pentru care Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F} are sens și să se simpifice această fracție.
Soluție.
Avem Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^3 - 9x^2 + 26x - 24 = x^3 - 2x^2 - 7x^2 + 14x + 12x-24=\left(x-2\right) \left(x^2-7x+12\right) = \left(x-2\right)\left(x-3\right)\left(x-4\right)} . Deci, fracția Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F} este bine definită pentru orice .
Avem Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^4 - 10x^3 + 35x^2 - 50x +24 = x^4-x^3 - 9x^3 +9x^2 + 26x^2 - 26x - 24x+24 = (x-1)\left(x^3 - 9x^2 + 26x - 24\right)} . Rezultă Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F = x-1} .