The value of `f(x)=x^4+4x^3+2x^2-4x+7,` when `x=cot((11pi)/8)` is _________

Explanation

`x= cot((11pi)/8) = cot(pi+(3pi)/8) = cot((3pi)/8) = sqrt2-1`

`:. x+1 = sqrt2`

`=>(x+1)^2 = 2`

`=>x^2+2x+1 = 2`

`=>x^2+2x-1 = 0`

Now, `f(x) = x^4+4x^3+2^2-4x+7`

`=x^2(x^2+4x+2)-4x+7`

`=x^2(x^2+2x-1)+2x^3+3x^2-4x+7`

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