Respuesta :
Answer:
Option 2 - [tex]x=\frac{7\pm3\sqrt{3}i}{2}[/tex]
Step-by-step explanation:
Given : Equation [tex](x-5)^2+3(x-5)+9=0[/tex]
To find : What is the solution of the equation ?
Solution :
Using substitution method,
Let y=x-5
[tex]y^2+3y+9=0[/tex]
Using quadratic formula, [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here, a=1, b=3 and c=9
[tex]y=\frac{-3\pm\sqrt{3^2-4(1)(9)}}{2(1)}[/tex]
[tex]y=\frac{-3\pm\sqrt{-27}}{2}[/tex]
[tex]y=\frac{-3\pm3\sqrt{3}i}{2}[/tex]
Substitute back,
[tex]x=\frac{-3\pm3\sqrt{3}i}{2}+5[/tex]
[tex]x=\frac{-3\pm3\sqrt{3}i+10}{2}[/tex]
[tex]x=\frac{7\pm3\sqrt{3}i}{2}[/tex]
Therefore, option 2 is correct.
Answer:
Option 2
Step-by-step explanation:
I just took the test and got it right.
