Răspuns:
3) 4[tex]x^{2}[/tex]-4x = 8+[tex]4\sqrt{2}[/tex]
4[tex]x^{2}[/tex]-4x-8-[tex]4\sqrt{2}[/tex] = 0 /:4
[tex]x^{2}[/tex]-x-2-[tex]\sqrt{2}[/tex] = 0
[tex]ax^{2}[/tex]+bx+c=0
Formula: x= (-b ± [tex]\sqrt{b^{2}-4ac }[/tex])/2a
x= [-(-1) ± [tex]\sqrt{(-1)^{2}-4*1(-2-\sqrt{2)} }[/tex]]/2
x= (1 ± [tex]\sqrt{1+8+4\sqrt{2} }[/tex])/2
x=(1 ± [tex]\sqrt{(1+\sqrt{8})^{2} }[/tex])/2
x= (1 ± 1+[tex]\sqrt{8}[/tex])/2
x= (1 ± 1+[tex]2\sqrt{2}[/tex])/2
x= (1+1+[tex]2\sqrt{2}[/tex])/2
x= [1-(1+[tex]2\sqrt{2}[/tex])]/2
x1 = 1+[tex]\sqrt{2}[/tex]
x2 = [tex]-\sqrt{2}[/tex]
Raspuns: B. {[tex]-\sqrt{2}[/tex];[tex]\sqrt{2}+1[/tex]}
