Solve {l}{P=a^{4}-3a^{3}b+4a^{2}b^{2}-5b^{3}}{Q=3a^{4}-4ab^{3}+7a^{3}b-2a^{2}b^{2}}{R=2a^{2}b^2-2a^3b-6a^4+3ab^3}

$$\left. \begin{array} { l } { P = a ^ { 4 } - 3 a ^ { 3 } b + 4 a ^ { 2 } b ^ { 2 } - 5 b ^ { 3 } } \\ { Q = 3 a ^ { 4 } - 4 a b ^ { 3 } + 7 a ^ { 3 } b - 2 a ^ { 2 } b ^ { 2 } } \\ { R = 2 a ^ { 2 } b ^ { 2 } - 2 a ^ { 3 } b - 6 a ^ { 4 } + 3 a b ^ { 3 } } \end{array} \right.$$

Solve for P, a, b, Q, R (complex solution)

$$P=a^{4}-5b^{3}-3ba^{3}+4\left(ab\right)^{2}$$

$$a\in \mathrm{C}$$

$$b\in \mathrm{C}$$

$$Q=a\left(3a^{3}-2ab^{2}-4b^{3}+7ba^{2}\right)$$

$$R=a\left(-6a^{3}+2ab^{2}+3b^{3}-2ba^{2}\right)$$

Solve for P, a, b, Q, R

$$P=a^{4}-5b^{3}-3ba^{3}+4\left(ab\right)^{2}$$

$$a\in \mathrm{R}$$

$$b\in \mathrm{R}$$

$$Q=a\left(3a^{3}-2ab^{2}-4b^{3}+7ba^{2}\right)$$

$$R=a\left(-6a^{3}+2ab^{2}+3b^{3}-2ba^{2}\right)$$