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

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

Réitigh do x.

$$x=\frac{355}{648}\approx 0.547839506$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} chun \left(x-\frac{1}{3}\right)^{3} a leathnú.

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

Úsáid an t-airí dáileach chun \frac{2}{5}x-1 a mhéadú faoi 2-x agus chun téarmaí comhchosúla a chumasc.

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

Chun an mhalairt ar \frac{9}{5}x-\frac{2}{5}x^{2}-2 a aimsiú, aimsigh an mhalairt ar gach téarma.

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

Comhcheangail \frac{1}{3}x agus -\frac{9}{5}x chun -\frac{22}{15}x a fháil.

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

Comhcheangail -x^{2} agus \frac{2}{5}x^{2} chun -\frac{3}{5}x^{2} a fháil.

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

Suimigh -\frac{1}{27} agus 2 chun \frac{53}{27} a fháil.

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

Úsáid an t-airí dáileach chun x a mhéadú faoi \frac{2}{5}x+3.

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

Chun an mhalairt ar \frac{2}{5}x^{2}+3x a aimsiú, aimsigh an mhalairt ar gach téarma.

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

Comhcheangail -\frac{3}{5}x^{2} agus -\frac{2}{5}x^{2} chun -x^{2} a fháil.

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

Comhcheangail -\frac{22}{15}x agus -3x chun -\frac{67}{15}x a fháil.

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

Úsáid an t-airí dáileach chun x^{2} a mhéadú faoi x-1.

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

Úsáid an t-airí dáileach chun -\frac{1}{3} a mhéadú faoi 2-x.

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

Bain x^{3} ón dá thaobh.

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

Comhcheangail x^{3} agus -x^{3} chun 0 a fháil.

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

Cuir x^{2} leis an dá thaobh.

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

Comhcheangail -x^{2} agus x^{2} chun 0 a fháil.

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

Bain \frac{1}{3}x ón dá thaobh.

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

Comhcheangail -\frac{67}{15}x agus -\frac{1}{3}x chun -\frac{24}{5}x a fháil.

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

Bain \frac{53}{27} ón dá thaobh.

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

Dealaigh \frac{53}{27} ó -\frac{2}{3} chun -\frac{71}{27} a fháil.

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

Iolraigh an dá thaobh faoi -\frac{5}{24}, an deilín de -\frac{24}{5}.

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

Méadaigh -\frac{71}{27} agus -\frac{5}{24} chun \frac{355}{648} a fháil.

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