Question 252552
For all real numbers {{{x}}}, the function {{{f(x)}}} satisfies {{{2f(x) + f(1-x) = x^2}}}
Find {{{f(5)}}}
<pre><font size = 4 color = "indigo"><b>
{{{2f(x)+f(1-x)=x^2}}}

Substitute {{{x=5}}}

{{{2f(5)+f(1-5)=5^2}}}
{{{2f(5)+f(-4)=25}}}


Substitute {{{x=-4}}}

{{{2f(-4)+f(1-(-4))=(-4)^2}}}
{{{2f(-4)+f(1+4)=16}}}
{{{2f(-4)+f(5)=16}}}

So we have this system of equations:

{{{syatem(2f(5)+f(-4)=25,2f(-4)+f(5)=16)}}}

Solve that and get:
{{{f(5)=34/3}}} and {{{f(-4)=7/3}}}

Edwin</pre>