NMTC 2015

Algebra Level 4

\(a,b,c,d,e\) are real numbers such that
\(a+4b+9c+16d+25e=1\)
\(4a+9b+16c+25d+36e=8\)
\(9a+16b+25c+36d+49e=23\).
Then the value of \(a+b+c+d+e\) is

Source: NMTC 2015 Inter Level.