Issolvi x(x+y)(y)-x^2=K(x^3+y^3)

$$x ( x + y ) ( y ) - x ^ { 2 } = K ( x ^ { 3 } + y ^ { 3 } )$$

Solvi għal K

$$\left\{\begin{matrix}K=\frac{x\left(xy-x+y^{2}\right)}{x^{3}+y^{3}}\text{, }&x\neq -y\\K\in \mathrm{R}\text{, }&x=0\text{ and }y=0\end{matrix}\right.$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika x b'x+y.

$$\left(x^{2}+xy\right)y-x^{2}=K\left(x^{3}+y^{3}\right)$$

Uża l-propjetà distributtiva biex timmultiplika x^{2}+xy b'y.

$$x^{2}y+xy^{2}-x^{2}=K\left(x^{3}+y^{3}\right)$$

Uża l-propjetà distributtiva biex timmultiplika K b'x^{3}+y^{3}.

$$x^{2}y+xy^{2}-x^{2}=Kx^{3}+Ky^{3}$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$Kx^{3}+Ky^{3}=x^{2}y+xy^{2}-x^{2}$$

Ikkombina t-termini kollha li fihom K.

$$\left(x^{3}+y^{3}\right)K=x^{2}y+xy^{2}-x^{2}$$

L-ekwazzjoni hija f'forma standard.

$$\left(x^{3}+y^{3}\right)K=yx^{2}+xy^{2}-x^{2}$$

Iddividi ż-żewġ naħat b'x^{3}+y^{3}.

$$\frac{\left(x^{3}+y^{3}\right)K}{x^{3}+y^{3}}=\frac{x\left(xy-x+y^{2}\right)}{x^{3}+y^{3}}$$

Meta tiddividi b'x^{3}+y^{3} titneħħa l-multiplikazzjoni b'x^{3}+y^{3}.

$$K=\frac{x\left(xy-x+y^{2}\right)}{x^{3}+y^{3}}$$

Iddividi x\left(-x+y^{2}+yx\right) b'x^{3}+y^{3}.

$$K=\frac{x\left(xy-x+y^{2}\right)}{\left(x+y\right)\left(x^{2}-xy+y^{2}\right)}$$