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

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

x खातीर सोडोवचें

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

लिनियर समिकरण सोडोवंक पांवडे

बायनोमियल प्रमेयाचो वापर करून \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} विस्तारावचें \left(x-\frac{1}{3}\right)^{3}.

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

वितरक गूणधर्माचो वापर करून \frac{2}{5}x-1 क 2-x न गुणचें आनी संज्ञां भशेन एकठावणी करची.

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

\frac{9}{5}x-\frac{2}{5}x^{2}-2 चो विरोधी सोदूंक, दरेक सज्ञेचो विरोधी सोदचो.

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

-\frac{22}{15}x मेळोवंक \frac{1}{3}x आनी -\frac{9}{5}x एकठांय करचें.

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

-\frac{3}{5}x^{2} मेळोवंक -x^{2} आनी \frac{2}{5}x^{2} एकठांय करचें.

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

\frac{53}{27} मेळोवंक -\frac{1}{27} आनी 2 ची बेरीज करची.

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

\frac{2}{5}x+3 न x गुणपाक विभाजक विशमाचो वापर करचो.

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

\frac{2}{5}x^{2}+3x चो विरोधी सोदूंक, दरेक सज्ञेचो विरोधी सोदचो.

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

-x^{2} मेळोवंक -\frac{3}{5}x^{2} आनी -\frac{2}{5}x^{2} एकठांय करचें.

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

-\frac{67}{15}x मेळोवंक -\frac{22}{15}x आनी -3x एकठांय करचें.

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

x-1 न x^{2} गुणपाक विभाजक विशमाचो वापर करचो.

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

2-x न -\frac{1}{3} गुणपाक विभाजक विशमाचो वापर करचो.

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

दोनूय कुशींतल्यान x^{3} वजा करचें.

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

0 मेळोवंक x^{3} आनी -x^{3} एकठांय करचें.

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

दोनूय वटांनी x^{2} जोडचे.

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

0 मेळोवंक -x^{2} आनी x^{2} एकठांय करचें.

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

दोनूय कुशींतल्यान \frac{1}{3}x वजा करचें.

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

-\frac{24}{5}x मेळोवंक -\frac{67}{15}x आनी -\frac{1}{3}x एकठांय करचें.

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

दोनूय कुशींतल्यान \frac{53}{27} वजा करचें.

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

-\frac{71}{27} मेळोवंक -\frac{2}{3} आनी \frac{53}{27} वजा करचे.

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

दोनूय कुशीनीं -\frac{5}{24} न गुणचें, -\frac{24}{5} चो रेसिप्रोकल.

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

\frac{355}{648} मेळोवंक -\frac{71}{27} आनी -\frac{5}{24} गुणचें.

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