Răspuns:
Explicație pas cu pas:
a)
[tex]x*x=(x-\sqrt{2} )(x-\sqrt{2}) +\sqrt{2} =(x-\sqrt{2} )^{2} +\sqrt{2} \\x*x=x\\\\(x-\sqrt{2} )^{2} +\sqrt{2}=x\\(x-\sqrt{2} )^{2} -(x-\sqrt{2})=0\\(x-\sqrt{2} )(x-\sqrt{2} -1)=0\\\\ x_{1} =\sqrt{2} \\x_{2} =1+\sqrt{2}[/tex]
f)
[tex](x-\sqrt{2} )^{2} +\sqrt{2}=x^{2} \\ \\ x^{2} -2\sqrt{2} x+2+\sqrt{2} -x^{2} =0\\ \\ 2\sqrt{2} x=2+\sqrt{2} \\ \\ x=\frac{2+\sqrt{2} }{2\sqrt{2} } =\frac{1+\sqrt{2} }{2}[/tex]
