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Binomická věta
Urči pomocí binomické věty:
\large \left( 1+\sqrt {3}\right) ^4
1+4\sqrt3+6\cdot\sqrt3^2+4\sqrt3^3+1\sqrt3^4=
=1+4\sqrt3+6\cdot3+12\sqrt3+6
\large = 25+16\sqrt {3}
1+4\sqrt3+6\cdot\sqrt3^2+4\sqrt3^3+1\sqrt3^4=
=1+4\sqrt3+6\cdot3+12\sqrt3+9
\large = 28+16\sqrt {3}
1+4\sqrt3+6\cdot\sqrt3^2+4\sqrt3^3+1\sqrt3^4=
=1+4\sqrt3+6\cdot3+8\sqrt3+9
\large = 28+12\sqrt {3}
1+4\sqrt3+6\cdot\sqrt3^2+4\sqrt3^3+1\sqrt3^4=
=1+4\sqrt3+6\cdot3+16\sqrt3+9
\large = 28+20\sqrt {3}