Question

X²-(√2+1)x+√2=0 помогите

Answer 1

$x^2-( sqrt{2}+1)x+ sqrt{2}=0\D=(-( sqrt{2}+1)^2-4*1* sqrt{2}=\=2+2 sqrt{2}+1-4 sqrt{2}=3-2 sqrt{2}\\x_1= frac{ sqrt{2}+1- sqrt{3-2 sqrt{2} } }{2} = frac{ sqrt{2}+1- sqrt{3- sqrt{8} } }{2}\\x_2= frac{ sqrt{2}+1+ sqrt{3-2 sqrt{2} } }{2} = frac{ sqrt{2}+1- sqrt{3- sqrt{8} } }{2}\\sqrt{3- sqrt{8}}= sqrt{ frac{3+ sqrt{3^2-8} }{2} }- sqrt{ frac{3- sqrt{3^2-8} }{2} }= sqrt{ frac{3+1}{2} }- sqrt{ frac{3-1}{2} }= sqrt{2}-1$
$x_1= frac{ sqrt{2}+1-( sqrt{2}-1 ) }{2}= frac{ sqrt{2}+1- sqrt{2}+1 }{2}= frac{2}{2}=1\\x_2= frac{ sqrt{2}+1+( sqrt{2}-1 ) }{2}= frac{ sqrt{2}+1+ sqrt{2}-1 }{2}= frac{2 sqrt{2} }{2}= sqrt{2}$

Ответ: 1 и √2