Verified answer

Ответ:

x⁴-73x²+576=01

x⁴-73x²+576-1=0

t²-73t+576-1=0

t²-73t+576=0

[tex]t = \frac{73 + \sqrt{3029} }{2} [/tex]

[tex]t = \frac{73 - \sqrt{3029} }{2} [/tex]

[tex]x {}^{2} = \frac{73 + \sqrt{3029} }{2} [/tex]

[tex]x {}^{2} = \frac{73 - \sqrt{3029} }{2} [/tex]

[tex]x = - \frac{ \sqrt{146 + 2 \sqrt{3029} } }{2} [/tex]

[tex]x = \frac{ \sqrt{146 + 2 \sqrt{3029} } }{2} [/tex]

[tex]x { }^{2} = \frac{73 - \sqrt{3029} }{2} [/tex]

[tex]x = - \frac{ \sqrt{146 + 2 \sqrt{3029} } }{2} [/tex]

[tex]x = \frac{ \sqrt{146 + 2 \sqrt{3029} } }{2} [/tex]

[tex]x = - \frac{ \sqrt{146 - 2 \sqrt{3029} } }{2} [/tex]

[tex]x = \frac{ \sqrt{146 - 2 \sqrt{3029} } }{2} [/tex]

Уравнение имеет 4 решения:

[tex] x_{1} = - \frac{ \sqrt{146 + 2 \sqrt{3029} } }{2} . x_{2} = - \frac{ \sqrt{146 - 2 \sqrt{3029} } }{2} . x_{3} = \frac{ \sqrt{146 - 2 \sqrt{3029} } }{2} . x_{4} = \frac{ \sqrt{146 + 2 \sqrt{3029} } }{2} [/tex]