Question

$$( x , y ) = x ^ { n } 3 - y ^ { n }$$

Answer

$$a=-(x*(1+x)*(1-x))/(e^4*IM*y^4*h*o^5*m*g*n^3*u^2*s*f^2*c*t*deg(r)),-(y-x^3)/(e^4*IM*y^4*h*o^5*m*g*n^3*u^2*s*f^2*c*t*deg(r))$$

Solution


Remove parentheses.
\[x,y={x}^{3}-{y}^{3}yahomogeneousfunct\imath onofdeg(r)ee\]
Regroup terms.
\[x,y={x}^{3}-{y}^{3}yahooooomgnnnuusffctee\imath r^{\circ}ee\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[x,y={x}^{3}-{y}^{3+1}ah{o}^{1+1+1+1+1}mg{n}^{1+1+1}{u}^{1+1}s{f}^{1+1}ctee\imath r^{\circ}ee\]
Simplify  \(3+1\)  to  \(4\).
\[x,y={x}^{3}-{y}^{4}ah{o}^{1+1+1+1+1}mg{n}^{1+1+1}{u}^{1+1}s{f}^{1+1}ctee\imath r^{\circ}ee\]
Simplify  \(1+1\)  to  \(2\).
\[x,y={x}^{3}-{y}^{4}ah{o}^{2+1+1+1}mg{n}^{1+1+1}{u}^{1+1}s{f}^{1+1}ctee\imath r^{\circ}ee\]
Simplify  \(2+1\)  to  \(3\).
\[x,y={x}^{3}-{y}^{4}ah{o}^{3+1+1}mg{n}^{1+1+1}{u}^{1+1}s{f}^{1+1}ctee\imath r^{\circ}ee\]
Simplify  \(3+1\)  to  \(4\).
\[x,y={x}^{3}-{y}^{4}ah{o}^{4+1}mg{n}^{1+1+1}{u}^{1+1}s{f}^{1+1}ctee\imath r^{\circ}ee\]
Simplify  \(4+1\)  to  \(5\).
\[x,y={x}^{3}-{y}^{4}ah{o}^{5}mg{n}^{1+1+1}{u}^{1+1}s{f}^{1+1}ctee\imath r^{\circ}ee\]
Simplify  \(1+1\)  to  \(2\).
\[x,y={x}^{3}-{y}^{4}ah{o}^{5}mg{n}^{2+1}{u}^{1+1}s{f}^{1+1}ctee\imath r^{\circ}ee\]
Simplify  \(2+1\)  to  \(3\).
\[x,y={x}^{3}-{y}^{4}ah{o}^{5}mg{n}^{3}{u}^{1+1}s{f}^{1+1}ctee\imath r^{\circ}ee\]
Simplify  \(1+1\)  to  \(2\).
\[x,y={x}^{3}-{y}^{4}ah{o}^{5}mg{n}^{3}{u}^{2}s{f}^{2}ctee\imath r^{\circ}ee\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[x,y={x}^{3}-{y}^{4}ah{o}^{5}mg{n}^{3}{u}^{2}s{f}^{2}ct{e}^{4}\imath r^{\circ}\]
Regroup terms.
\[x,y={x}^{3}-{e}^{4}\imath {y}^{4}ah{o}^{5}mg{n}^{3}{u}^{2}s{f}^{2}ctdeg(r)\]
Switch sides.
\[{x}^{3}-{e}^{4}\imath {y}^{4}ah{o}^{5}mg{n}^{3}{u}^{2}s{f}^{2}ctdeg(r)=x,y\]
Break down the problem into these 2 equations.
\[{x}^{3}-{e}^{4}\imath {y}^{4}ah{o}^{5}mg{n}^{3}{u}^{2}s{f}^{2}ctdeg(r)=x\]
\[{x}^{3}-{e}^{4}\imath {y}^{4}ah{o}^{5}mg{n}^{3}{u}^{2}s{f}^{2}ctdeg(r)=y\]
Solve the 1st equation: \({x}^{3}-{e}^{4}\imath {y}^{4}ah{o}^{5}mg{n}^{3}{u}^{2}s{f}^{2}ctdeg(r)=x\).
\[a=-\frac{x(1+x)(1-x)}{{e}^{4}\imath {y}^{4}h{o}^{5}mg{n}^{3}{u}^{2}s{f}^{2}ctdeg(r)}\]
Solve the 2nd equation: \({x}^{3}-{e}^{4}\imath {y}^{4}ah{o}^{5}mg{n}^{3}{u}^{2}s{f}^{2}ctdeg(r)=y\).
\[a=-\frac{y-{x}^{3}}{{e}^{4}\imath {y}^{4}h{o}^{5}mg{n}^{3}{u}^{2}s{f}^{2}ctdeg(r)}\]
Collect all solutions.
\[a=-\frac{x(1+x)(1-x)}{{e}^{4}\imath {y}^{4}h{o}^{5}mg{n}^{3}{u}^{2}s{f}^{2}ctdeg(r)},-\frac{y-{x}^{3}}{{e}^{4}\imath {y}^{4}h{o}^{5}mg{n}^{3}{u}^{2}s{f}^{2}ctdeg(r)}\]