Respuesta :
Answer:
Y = 2+- square root of 6
Step-by-step explanation:
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Lets solve ~
Let's calculate its discriminant ~
[tex]\qquad \sf \dashrightarrow \: {y}^{2} -4y - 2=0[/tex]
- a = 1
- b = -4
- c = -2
[tex]\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]
[tex]\qquad \sf \dashrightarrow \: d = (-4) {}^{2} - (4 \times 1\times - 2)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 16 - ( - 8)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 24[/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt {d }= 2 \sqrt{6} [/tex]
So, by quadratic formula :
[tex]\qquad \sf \dashrightarrow \: y= \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \: y = \dfrac{ - {(-4)}^{} \pm 2\sqrt{6} }{2 ×1} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:y=\pm \cfrac{2(2\pm\sqrt{6} }{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:y= { 2+\sqrt{6}}{} \: \: and \: \: t = {2-\sqrt{6}}{} [/tex]