Riješi (x-1/3)^3-(2/5x-1)(2-x)-x(2/5x+3)=x^2(x-1)-1/3(2-x)

$$( x - \frac { 1 } { 3 } ) ^ { 3 } - ( \frac { 2 } { 5 } x - 1 ) ( 2 - x ) - x ( \frac { 2 } { 5 } x + 3 ) = x ^ { 2 } ( x - 1 ) - \frac { 1 } { 3 } ( 2 - x )$$

Riješite za x

$$x=\frac{355}{648}\approx 0,547839506$$

Koraci za rješavanje linearne jednačine

Koristite binomnu teoremu \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} da biste proširili \left(x-\frac{1}{3}\right)^{3}.

$$x^{3}-x^{2}+\frac{1}{3}x-\frac{1}{27}-\left(\frac{2}{5}x-1\right)\left(2-x\right)-x\left(\frac{2}{5}x+3\right)=x^{2}\left(x-1\right)-\frac{1}{3}\left(2-x\right)$$

Koristite svojstvo distributivnosti da biste pomnožili \frac{2}{5}x-1 s 2-x i kombinirali slične pojmove.

$$x^{3}-x^{2}+\frac{1}{3}x-\frac{1}{27}-\left(\frac{9}{5}x-\frac{2}{5}x^{2}-2\right)-x\left(\frac{2}{5}x+3\right)=x^{2}\left(x-1\right)-\frac{1}{3}\left(2-x\right)$$

Da biste pronašli suprotnu vrijednost od \frac{9}{5}x-\frac{2}{5}x^{2}-2, pronađite suprotnu vrijednost svakog izraza.

$$x^{3}-x^{2}+\frac{1}{3}x-\frac{1}{27}-\frac{9}{5}x+\frac{2}{5}x^{2}+2-x\left(\frac{2}{5}x+3\right)=x^{2}\left(x-1\right)-\frac{1}{3}\left(2-x\right)$$

Kombinirajte \frac{1}{3}x i -\frac{9}{5}x da biste dobili -\frac{22}{15}x.

$$x^{3}-x^{2}-\frac{22}{15}x-\frac{1}{27}+\frac{2}{5}x^{2}+2-x\left(\frac{2}{5}x+3\right)=x^{2}\left(x-1\right)-\frac{1}{3}\left(2-x\right)$$

Kombinirajte -x^{2} i \frac{2}{5}x^{2} da biste dobili -\frac{3}{5}x^{2}.

$$x^{3}-\frac{3}{5}x^{2}-\frac{22}{15}x-\frac{1}{27}+2-x\left(\frac{2}{5}x+3\right)=x^{2}\left(x-1\right)-\frac{1}{3}\left(2-x\right)$$

Saberite -\frac{1}{27} i 2 da biste dobili \frac{53}{27}.

$$x^{3}-\frac{3}{5}x^{2}-\frac{22}{15}x+\frac{53}{27}-x\left(\frac{2}{5}x+3\right)=x^{2}\left(x-1\right)-\frac{1}{3}\left(2-x\right)$$

Koristite distributivno svojstvo da biste pomnožili x sa \frac{2}{5}x+3.

$$x^{3}-\frac{3}{5}x^{2}-\frac{22}{15}x+\frac{53}{27}-\left(\frac{2}{5}x^{2}+3x\right)=x^{2}\left(x-1\right)-\frac{1}{3}\left(2-x\right)$$

Da biste pronašli suprotnu vrijednost od \frac{2}{5}x^{2}+3x, pronađite suprotnu vrijednost svakog izraza.

$$x^{3}-\frac{3}{5}x^{2}-\frac{22}{15}x+\frac{53}{27}-\frac{2}{5}x^{2}-3x=x^{2}\left(x-1\right)-\frac{1}{3}\left(2-x\right)$$

Kombinirajte -\frac{3}{5}x^{2} i -\frac{2}{5}x^{2} da biste dobili -x^{2}.

$$x^{3}-x^{2}-\frac{22}{15}x+\frac{53}{27}-3x=x^{2}\left(x-1\right)-\frac{1}{3}\left(2-x\right)$$

Kombinirajte -\frac{22}{15}x i -3x da biste dobili -\frac{67}{15}x.

$$x^{3}-x^{2}-\frac{67}{15}x+\frac{53}{27}=x^{2}\left(x-1\right)-\frac{1}{3}\left(2-x\right)$$

Koristite distributivno svojstvo da biste pomnožili x^{2} sa x-1.

$$x^{3}-x^{2}-\frac{67}{15}x+\frac{53}{27}=x^{3}-x^{2}-\frac{1}{3}\left(2-x\right)$$

Koristite distributivno svojstvo da biste pomnožili -\frac{1}{3} sa 2-x.

$$x^{3}-x^{2}-\frac{67}{15}x+\frac{53}{27}=x^{3}-x^{2}-\frac{2}{3}+\frac{1}{3}x$$

Oduzmite x^{3} s obje strane.

$$x^{3}-x^{2}-\frac{67}{15}x+\frac{53}{27}-x^{3}=-x^{2}-\frac{2}{3}+\frac{1}{3}x$$

Kombinirajte x^{3} i -x^{3} da biste dobili 0.

$$-x^{2}-\frac{67}{15}x+\frac{53}{27}=-x^{2}-\frac{2}{3}+\frac{1}{3}x$$

Dodajte x^{2} na obje strane.

$$-x^{2}-\frac{67}{15}x+\frac{53}{27}+x^{2}=-\frac{2}{3}+\frac{1}{3}x$$

Kombinirajte -x^{2} i x^{2} da biste dobili 0.

$$-\frac{67}{15}x+\frac{53}{27}=-\frac{2}{3}+\frac{1}{3}x$$

Oduzmite \frac{1}{3}x s obje strane.

$$-\frac{67}{15}x+\frac{53}{27}-\frac{1}{3}x=-\frac{2}{3}$$

Kombinirajte -\frac{67}{15}x i -\frac{1}{3}x da biste dobili -\frac{24}{5}x.

$$-\frac{24}{5}x+\frac{53}{27}=-\frac{2}{3}$$

Oduzmite \frac{53}{27} s obje strane.

$$-\frac{24}{5}x=-\frac{2}{3}-\frac{53}{27}$$

Oduzmite \frac{53}{27} od -\frac{2}{3} da biste dobili -\frac{71}{27}.

$$-\frac{24}{5}x=-\frac{71}{27}$$

Pomnožite obje strane s -\frac{5}{24}, recipročnom vrijednošću od -\frac{24}{5}.

$$x=-\frac{71}{27}\left(-\frac{5}{24}\right)$$

Pomnožite -\frac{71}{27} i -\frac{5}{24} da biste dobili \frac{355}{648}.

$$x=\frac{355}{648}$$