Question

(8x+3)²-x^4=8x²+16 Решить уравнение

Answer 1

(8х+3)²-х⁴=8х²+16;

64х²+48х+9-х⁴=8х²+16;

х⁴-56х²-48х+7=0;
По схеме Горнера:

α=-1;

(х⁴-56х²-48х+7):(х+1)=х³-х²-55х+7;

α=-7;

(х³-х²-55х+7):(х+7)=х²-8х+1;

х²-8х+1=0;

D=64-4=60; √D=2√15;

x₁=4-√15;

x₂=4+√15.

(x-(4-√15))(x-(4+√15))(x+7)(x+1)=0;

x=4±√15; -7; -1.

Answer 2

(8х+3)²-х⁴=8х²+16;

64х²+48х+9-х⁴=8х²+16;

х⁴-56х²-48х+7=0;
По схеме Горнера:

α=-1;

(х⁴-56х²-48х+7):(х+1)=х³-х²-55х+7;

α=-7;

(х³-х²-55х+7):(х+7)=х²-8х+1;

х²-8х+1=0;

D=64-4=60; √D=2√15;

x₁=4-√15;

x₂=4+√15.

(x-(4-√15))(x-(4+√15))(x+7)(x+1)=0;

x=4±√15; -7; -1.