Calling Sequence solve(eqns, vars)

Parameters

 eqns - equations (as for solve), but with radicals vars - variables (as for solve)

Description

 • The solve function will solve equations with radicals by using new auxiliary variables and adding new equations.
 • In some cases the resulting problem will be a system of equations, but in many simple cases radical equations will be handled with transformations and post-processing. For example, the equation ${x}^{2}+\sqrt{x+1}=3$ is transformed into ${z}^{4}-2{z}^{2}+z=2$ using the substitution $x={z}^{2}-1$.

Examples

 > $\mathrm{solve}\left(\mathrm{sqrt}\left(x+1\right)-\mathrm{sqrt}\left(x-1\right)=a,x\right)$
 $\frac{{{a}}^{{4}}{+}{4}}{{4}{}{{a}}^{{2}}}$ (1)
 > $\mathrm{solve}\left(x+\mathrm{sqrt}\left(x\right)-2,x\right)$
 ${1}$ (2)
 > $\mathrm{solve}\left(x+\mathrm{sqrt}\left(x\right)+{x}^{\frac{1}{3}}=3,x\right)$
 ${1}$ (3)
 > $\mathrm{solve}\left(\mathrm{sqrt}\left(x\right)+\mathrm{sqrt}\left(x+1\right)=3\right)$
 $\frac{{16}}{{9}}$ (4)
 > $\mathrm{solve}\left(\left\{x-y+1,\mathrm{sqrt}\left(x\right)+\mathrm{sqrt}\left(y\right)-2\right\},\left\{x,y\right\}\right)$
 $\left\{{x}{=}\frac{{9}}{{16}}{,}{y}{=}\frac{{25}}{{16}}\right\}$ (5)