Coinciding conundrum

[Theren]

Hello everyone,

I've been struggling on this problem for a bit now and can't find any books to help me with it.

f(x)= x² - 6x + 2
g(x) = 2 - x²

(i) Find the two values of x for which f(x) and g(x) coincide.
(ii) Find the values of f(x) which correspond to the values of x in part (i)

I'd really appreciate some guidance on how to solve these questions or any steps to help with the questions.

 

[pka]

Hello everyone, can't find any books to help me with it.
f(x)= x² - 6x + 2
g(x) = 2 - x²
(i) Find the two values of x for which f(x) and g(x) coincide.
(ii) Find the values of f(x) which correspond to the values of x in part (i)

Can you solve \(\displaystyle 2-x^2=x^2-6x+2~?\)

 

[Theren]

Can you solve \(\displaystyle 2-x^2=x^2-6x+2~?\)

Would any of these be correct?
[FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math-italic]x² [/FONT][FONT=MathJax_Main]= [/FONT][FONT=MathJax_Math-italic]x²[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]

1. + x² [/FONT][FONT=MathJax_Main]on each side making 2 = 2x²[/FONT][FONT=MathJax_Main] - 6x + 2
2. +6x on each side making 2 + 6x = 2x² + 2
3. -2 on each side making 6x = 2x²

​Second Attempt

[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Math-italic]x² [/FONT][FONT=MathJax_Main]= [/FONT][FONT=MathJax_Math-italic]x²[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]6[/FONT][FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]

1. + [/FONT][FONT=MathJax_Main]x² [/FONT][FONT=MathJax_Main]on each side making 2 = 2x²[/FONT][FONT=MathJax_Main] - 6x + 2
2. [/FONT]-2 [FONT=MathJax_Main]on each side making[/FONT]2x²- 6x = 0
3. Put the equation into the quadratic formula giving the result of x = 3 and x = 0