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

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

Atrast x

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

Lineāra vienādojuma risināšanas darbības

Lietojiet Ņūtona binomu \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3}, lai izvērstu \left(x-\frac{1}{3}\right)^{3}.

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

Izmantojiet distributīvo īpašību, lai reizinātu \frac{2}{5}x-1 ar 2-x un apvienotu līdzīgos locekļus.

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

Lai atrastu \frac{9}{5}x-\frac{2}{5}x^{2}-2 pretējo vērtību, atrodiet katra locekļa pretējo vērtību.

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

Savelciet \frac{1}{3}x un -\frac{9}{5}x, lai iegūtu -\frac{22}{15}x.

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

Savelciet -x^{2} un \frac{2}{5}x^{2}, lai iegūtu -\frac{3}{5}x^{2}.

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

Saskaitiet -\frac{1}{27} un 2, lai iegūtu \frac{53}{27}.

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

Izmantojiet distributīvo īpašību, lai reizinātu x ar \frac{2}{5}x+3.

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

Lai atrastu \frac{2}{5}x^{2}+3x pretējo vērtību, atrodiet katra locekļa pretējo vērtību.

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

Savelciet -\frac{3}{5}x^{2} un -\frac{2}{5}x^{2}, lai iegūtu -x^{2}.

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

Savelciet -\frac{22}{15}x un -3x, lai iegūtu -\frac{67}{15}x.

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

Izmantojiet distributīvo īpašību, lai reizinātu x^{2} ar x-1.

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

Izmantojiet distributīvo īpašību, lai reizinātu -\frac{1}{3} ar 2-x.

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

Atņemiet x^{3} no abām pusēm.

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

Savelciet x^{3} un -x^{3}, lai iegūtu 0.

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

Pievienot x^{2} abās pusēs.

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

Savelciet -x^{2} un x^{2}, lai iegūtu 0.

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

Atņemiet \frac{1}{3}x no abām pusēm.

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

Savelciet -\frac{67}{15}x un -\frac{1}{3}x, lai iegūtu -\frac{24}{5}x.

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

Atņemiet \frac{53}{27} no abām pusēm.

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

Atņemiet \frac{53}{27} no -\frac{2}{3}, lai iegūtu -\frac{71}{27}.

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

Reiziniet abās puses ar -\frac{5}{24}, abpusēju -\frac{24}{5} vērtību.

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

Reiziniet -\frac{71}{27} un -\frac{5}{24}, lai iegūtu \frac{355}{648}.

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