Risolvere la seguente disequazione frazionaria: $\displaystyle \frac{1}{x^2-x}-\frac{1}{x}\ge\frac{2}{x-1}$ SOLUZIONE $\displaystyle \frac{1}{x(x-1)}-\frac{1}{x}\ge\frac{2}{x-1}$ $\displaystyle \frac{1}{x(x-1)}-\frac{1}{x}-\frac{2}{x-1}\ge0$ $\displaystyle \frac{1-1(x-1)-2x}{x(x-1)}\ge0$ $\displaystyle \frac{1-x+1-2x}{x(x-1)}\ge0$ $\displaystyle \frac{2-3x}{x(x-1)}\ge0$ Studio del…
Risolvere la seguente equazione frazionaria di primo grado: $\displaystyle \frac{1}{x}+\frac{1}{x-2}=\frac{2}{x-3}$ $\displaystyle \frac{(x-2)(x-3)+x(x-3)}{x(x-2)(x-3)}=\frac{2[x(x-2)]}{x(x-2)(x-3)}$ $\displaystyle \frac{x^2-3x-2x+6+x^2-3x}{x(x-2)(x-3)}=\frac{2x^2-4x}{x(x-2)(x-3)}$ C.E: $x\neq 0$, $x\neq 2$, $x\neq…
Scomporre i seguenti polinomi: 1) $\displaystyle x^3-x^2+\frac{1}{3}x-\frac{1}{27}=\left(x-\frac{1}{3}\right)^3$ 2) $\displaystyle a^3-6a^2+12a-8=(a-2)^3$ 3) $\displaystyle 27a^6-54a^4+18a^2-8=(3a^2-2)^3$ 4) $\displaystyle 0,125t^3-3t^2+24t-64=(0,5t-4)^3$ 5) $\displaystyle x^{6n}-6x^{4n}+12x^{2n}-8=(x^{2n}-2)^3$ 6)…
Scomporre i seguenti trinomi caratteristici di primo tipo: 1) $\displaystyle x^2-3x-18=(x-6)(x+3)$ prodotto $=-18$ somma $=-3$ I numeri che danno prodotto $-18$…
:Scomporre i seguenti polinomi 1) $\displaystyle 4y^2+4xy+12yz+x^2+6xz+9z^2=$ $\displaystyle =(2y+x+3z)^2$. 2) $\displaystyle \frac{1}{4}a^2-2ab-ac+4b^2+4bc+c^2=$ $\displaystyle =\left(-\frac{1}{2}a+2b+c\right)^2$. 3) $\displaystyle \frac{1}{4}a^6-a^5+a^4+2a^3-4a^2+4=$ $\displaystyle =\left(\frac{1}{2}a^3-a^2+2\right)^2$. 4)…
Scomporre i seguenti polinomi: 1) $\displaystyle a^6-b^3=(a^2-b)(a^4+a^{2}b+b^2)$ 2) $\displaystyle -\frac{1}{8}a^3+8=$ $\displaystyle =\left(2-\frac{1}{2}a\right)\left(4+a+\frac{1}{4}a^2\right)$ 3) $\displaystyle x^6-8y^3=(x^2-2y)(x^4+2x^{2}y+4y^2)$ 4) $\displaystyle a^3+27=(a+3)(a^2-3a+9)$ 5) $\displaystyle…
Scomporre i seguenti trinomi caratteristici di secondo tipo: 1) $\displaystyle 10x^2+7x-6=$ $\displaystyle = 10x^2-5x+12x-6=$ $\displaystyle =5x(2x-1)+6(2x-1)=$ $\displaystyle =(2x-1)(5x+6)$. 2) $\displaystyle…
Scomporre i seguenti polinomi: 1) $\displaystyle -a^4+b^2=(b+a^2)(b-a^2)$ 2) $\displaystyle \frac{1}{4}x^6-\frac{1}{9}y^2=\left(\frac{1}{2}x^3+\frac{1}{3}y\right)\left(\frac{1}{2}x^3-\frac{1}{3}y\right)$ 3) $\displaystyle x^{2n}-y^4=(x^n+y^2)(x^n-y^2)$ 4) $\displaystyle a^{2n+2}-1=a^{2(n+1)}-1=(a^{n+1}+1)(a^{n+1}-1)$ 5) $\displaystyle -81a^4+4^{-2}=-81a^4+\left(\frac{1}{4}\right)^2=$ $\displaystyle=\left(\frac{1}{4}+9a^2\right)\left(\frac{1}{4}-9a^2\right)=$…
Scomporre i seguenti polinomi: 1) $\displaystyle x^4+2x^2+1=(x^2+1)^2$ 2) $\displaystyle 4a^2-4a+1=(2a-1)^2$ 3) $\displaystyle 16x^4+8x^2+1=(4x^2+1)^2$ 4) $\displaystyle a^2-6a+9=(a-3)^2$ 5) $\displaystyle \frac{25}{4}x^6-5x^3+1=\left(\frac{5}{2}x^3-1\right)^2$ 6)…
Scomporre i seguenti polinomi mediante raccoglimento totale e raccoglimento parziale-totale: 1) $\displaystyle 50x^2-10x-5x^3=$ $\displaystyle =5x(10x-2-x^2)$ 2) $\displaystyle 4x^2y^2+6xy=$ $\displaystyle =2xy(2xy+3)$…
