Let [tex]u= x^{2} [/tex]
so our equation becomes [tex]u^{2}-4u+2=0[/tex]
subtract 2 from both sides of the equation [tex]u^{2}-4u = -2[/tex]
Take half of b, square the result and add to both sides [tex]\frac{1}{2}(-4) = -2[/tex] (remember -2 it will be used when factoring the trinomial)
(-2)² = 4
[tex]u^{2}-4u+4=-2+4[/tex]
Factor trinomial and simplify right side [tex](u-2)^{2}=2[/tex] note:-2 is in the factor
Square root both sides (must use +/-): [tex]u-2=+/- \sqrt{2} [/tex]
Add 2 to both sides: [tex]u = 2 +/- \sqrt{2} [/tex]
:-( not finish yet
[tex]u= x^{2} [/tex]
[tex]2+ \sqrt{2} = x^{2} [/tex] and [tex]2- \sqrt{2} = x^{2} [/tex]
Final answers:
[tex]x= +/-\sqrt{2+ \sqrt{2}} [/tex] and [tex]x = +/-\sqrt{2- \sqrt{2} }[/tex]
[tex]\sqrt{2+\sqrt{2}},-\sqrt{2+\sqrt{2}},\sqrt{2-\sqrt{2}},-\sqrt{2-\sqrt{2}}[/tex]
Think of it as four possible answers:
