Answer:
1) [tex]\bold{x=2\sqrt6+5\quad\ \vee\quad x=-2\sqrt6+5}[/tex]
2) [tex]\bold{x=3\quad\vee\quad x=-1}[/tex]
Step-by-step explanation:
1)
[tex]x^2 - 10x + 1 = 0\\\\x^2 - 2\cdot x\cdot5 +5^2-5^2 + 1 = 0\\\\(x-5)^2-25+1=0\\\\(x-5)^2=24\\\\x-5=\sqrt{24}\qquad\vee\qquad x-5=-\sqrt{24}\\\\ x=2\sqrt6+5\qquad\vee\qquad x=-2\sqrt6+5[/tex]
2)
[tex]4x^2-8x=12\\\\x^2-2x=3\\\\x^2-2\cdot x\cdot1+1^2-1^2=3\\\\(x-1)^2-1=3\\\\(x-1)^2=4\\\\x-1=2\qquad\vee\qquad x-1=-2\\\\x=3\qquad\vee\qquad x=-1[/tex]
