Don't think about a+b+c+da+b+c+d as a known equation!

Algebra Level 3

{a+b+cd=1a+bc+d=2ab+c+d=3a+b+c+d=4\begin{cases} a+b+c-d = 1 \\ a+b-c+d = 2 \\ a-b+c+d = 3 \\ -a+b+c+d = 4 \end{cases}

If the system of equations above holds true for the positive real number of a,b,c,d a, b, c, d, then find the value of the expression below.

8a2+9b2+12c2+13d2\begin{aligned} 8a^2 + 9b^2 + 12c^2 + 13d^2 \end{aligned}


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