What is f(x)(f(x))=x^2+x+1 ?

The solution to f(x)(f(x))=x^2+x+1 is Hyperbola with (h,k)=(-1/2 ,0),a=(sqrt(3))/2 ,b=(sqrt(3))/2

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f(x)(f(x))=x^2+x+1

f (x) (f (x)) = x^{2} + x + 1

(h, k) = (- \frac{1}{2}, 0), a = \frac{3}{2}, b = \frac{3}{2}

Solution steps

yy = x^{2} + x + 1

Rewrite

yy - x^{2} - x - 1 = 0

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{3}{2} ) ^{2}} - \frac{( x - ( - \frac{1}{2} ) ) ^{2}}{( \frac{3}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{1}{2}, 0), a = \frac{3}{2}, b = \frac{3}{2}

4 x^{2} - 9 y^{2} - 16 x + 54 y - 101 = 0

y^{2} - x^{2} = 81

36 + y^{2} = x^{2}

(16) x^{2} - (225) y^{2} + (0) x + (- 2250) y + (2025) = 0

5 x^{2} - 3 y^{2} + 10 x - 12 y = 22

What is f(x)(f(x))=x^2+x+1 ?
The solution to f(x)(f(x))=x^2+x+1 is Hyperbola with (h,k)=(-1/2 ,0),a=(sqrt(3))/2 ,b=(sqrt(3))/2