álgebra: ecuacions polinomiques II

ax^{p}+ax^{q} = ax^{[..(1)..[ p+(-q) ]..(1)..]+q}


ax^{p}+ax^{q} = c


x = (c/a)^{( 1/( [..(1)..[ p+(-q) ]..(1)..]+q ) )}


ax^{p}+bx^{q} = ax^{[..(b/a)..[ p+(-q) ]..(b/a)..]+q}


ax^{p}+bx^{q} = c


x = (c/a)^{( 1/( [..(b/a)..[ p+(-q) ]..(b/a)..]+q ) )}


x^{p}+mx = c


x = c^{( 1/( [..(m)..[ p+(-1) ]..(m)..]+1 ) )}


x = c^{( 1/( log[x](x^{(p+(-1))}+m)+1 ) )}


x^{p}+mx = (1+(-m))^{(1/(p+(-1)))} <==> ...
... log[x](x^{(p+(-1))}+m) = 0 <==> x = (1+(-m))^{(1/(p+(-1)))}


x^{p}+mx = 2m^{(p/(p+(-1)))} <==> ...
... log[x](x^{(p+(-1))}+m) = log[x](2m) <==> x = m^{(1/(p+(-1)))}


k·x^{p}+(mk)·x^{q} = c


x = (c/k)^{( 1/( [..(m)..[ p+(-q) ]..(m)..]+q ) )}


k·x^{p}+(mk)·x^{q} = k·(1+(-m))^{(q/(p+(-q)))} <==> ...
... log[x](x^{(p+(-q))}+m) = 0 <==> x = (1+(-m))^{(1/(p+(-q)))}


k·x^{p}+(mk)·x^{q} = (2k)·m^{(p/(p+(-q)))} <==> ...
... log[x](x^{(p+(-q))}+m) = log[x](2m) <==> x = m^{(1/(p+(-q)))}


x^{4}+4x = c


x = c^{( 1/( [..(4)..[3]..(4)..]+1 ) )}


x = c^{( 1/( log[x](x^{3}+4)+1 ) )}


x^{4}+4x = (-3)^{(1/3)} <==> log[x](x^{3}+4) = 0 <==> x = (-3)^{(1/3)}


x^{4}+4x = 2·4^{(4/3)} <==> log[x](x^{3}+4) = log[x](8) <==> x = 4^{(1/3)}


x^{4}+x = 0 <==> x = e^{(1/3)·(pi·i)}


4x^{8}+12x = c


x = (c/4)^{( 1/( [..(3)..[7]..(3)..]+1 ) )}


x = (c/4)^{( 1/( log[x](x^{7}+3)+1 ) )}


4x^{8}+12x = 4·(-2)^{(1/7)} <==> log[x](x^{7}+3) = 0 <==> x = (-2)^{(1/7)}


4x^{8}+12x = 8·3^{(8/7)} <==> log[x](x^{7}+3) = log[x](6) <==> x = 3^{(1/7)}


x^{8}+x = 0 <==> x = e^{(1/7)·(pi·i)}


8x^{8}+32x^{2} = c


x = (c/8)^{( 1/( [..(4)..[6]..(4)..]+2 ) )}


x = (c/8)^{( 1/( log[x](x^{6}+4)+2 ) )}


8x^{8}+32x^{2} = 8·(-3)^{(1/3)} <==> log[x](x^{6}+4) = 0 <==> x = (-3)^{(1/6)}


8x^{8}+32x^{2} = 16·4^{(4/3)} <==> log[x](x^{6}+4) = log[x](8) <==> x = 4^{(1/6)}


x^{8}+x^{2} = 0 <==> x = e^{(1/6)·(pi·i)}