Issolvi (x-y)^3=A(x+y).text{provethat}(2x+y)dy/dx=x+2y

$$( x - y ) ^ { 3 } = A ( x + y ) . \text { prove that } ( 2 x + y ) \frac { d y } { d x } = x + 2 y$$

Solvi għal A

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża teorema binomjali \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} biex tespandi \left(x-y\right)^{3}.

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

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

$$x^{3}-3x^{2}y+3xy^{2}-y^{3}=Ax+Ay$$

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

$$Ax+Ay=x^{3}-3x^{2}y+3xy^{2}-y^{3}$$

Ikkombina t-termini kollha li fihom A.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'x+y.

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

Meta tiddividi b'x+y titneħħa l-multiplikazzjoni b'x+y.

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