In[3]:= eqn = x^2 + 3x == 2 2 Out[3]= 3 x + x == 2 In[4]:= Roots[eqn, x] -3 - Sqrt[17] -3 + Sqrt[17] Out[4]= x == ------------- || x == ------------- 2 2 In[5]:= Solve[eqn, x] -3 - Sqrt[17] -3 + Sqrt[17] Out[5]= {{x -> -------------}, {x -> -------------}} 2 2 In[6]:= x^2 + 3x /. % 2 3 (-3 - Sqrt[17]) (-3 - Sqrt[17]) Out[6]= {----------------- + ----------------, 2 4 2 3 (-3 + Sqrt[17]) (-3 + Sqrt[17]) > ----------------- + ----------------} 2 4 In[7]:= Simplify[ % ] Out[7]= {2, 2} In[8]:= N[ Out[4] ] Out[8]= x == -3.56155 || x == 0.561553 In[9]:= NSolve[ eqn, x ] Out[9]= {{x -> -3.56155}, {x -> 0.561553}} In[10]:= poly = Product[ x-a , {a,1,5} ] Out[10]= (-5 + x) (-4 + x) (-3 + x) (-2 + x) (-1 + x) In[11]:= PolyEx = Expand[poly] 2 3 4 5 Out[11]= -120 + 274 x - 225 x + 85 x - 15 x + x In[15]:= Roots [ PolyEx==0, x] Out[15]= x == 5 || x == 4 || x == 3 || x == 2 || x == 1 In[16]:= polyFive = x^5 + 5x + 1 == 0 5 Out[16]= 1 + 5 x + x == 0 In[17]:= Solve[ polyFive, x ] 5 Out[17]= {ToRules[Roots[5 x + x == -1, x]]} In[18]:= N [ % ] Out[18]= {{x -> -1.0045 - 1.06095 I}, {x -> -1.0045 + 1.06095 I}, > {x -> -0.199936}, {x -> 1.10447 - 1.05983 I}, {x -> 1.10447 + 1.05983 I}} In[19]:= NSolve [ polyFive ] Out[19]= {{x -> -1.0045 - 1.06095 I}, {x -> -1.0045 + 1.06095 I}, > {x -> -0.199936}, {x -> 1.10447 - 1.05983 I}, {x -> 1.10447 + 1.05983 I}} In[20]:= twoEqns = { a x + b y 1 == 1, x - y == 2 } Out[20]= {a x + b y == 1, x - y == 2} In[21]:= Solve[ twoEqns, {x,y} ] -1 + 2 a -1 + 2 a Out[21]= {{x -> 2 - --------, y -> -(--------)}} a + b a + b In[22]:= Eliminate[ twoEqns, y ] Out[22]= a x == 1 + 2 b - b x In[23]:= Reduce [ twoEqns, {x,y} ] 1 1 Out[23]= x == 2 + y && b == -(-) && a == - || 2 2 1 + 2 b 1 - 2 a > a + b != 0 && x == ------- && y == ------- a + b a + b