Algebra

First, let's simplify the equation we are given. We get

\(10x^2 + 10x - 1\\ ab = -1/10\\ 2ab = -2/10 = -1/5\)

Now, take a + b  =  -1

Squaring both sides, we get

\(a^2 + 2ab + b^2  = 1 \\ a^2 - 1/5 + b^2  = 1 \\ a^2 + b^2  = 1 + 1/5  =  6/5\)

\((a -4) / ( b -4) + ( b -4) / (a -4) = [ (a - 4)^2 + ( b -4)^2] ] ' [ (a -4) ( b-4) ] = \\ [ a^2 - 8a +16 + b^2 - 8b + 16 ] / [ ab - 4(a + b) +16 ] = \\ [ (a^2 + b^2) - 8(a + b) + 32 ] / [ ab - 4 (a + b) + 16 ] =\\ [ 6/5 - 8 (-1) + 32 ] [ -1/10 - 4 (-1) + 16 ] = \\ [ 6/5 + 40 ] / [ 20 - 1/10] = 20497 / 25\)

The answer is \(20497 / 25\)

Thanks! :)