11−x−x2Step 1
=1(x−1+√52)(x−1−√52)Step 2
=x+1+√52(x−1+√52)(x+1+√52)×x+1−√52(x−1−√52)(x+1−√52)Step 3
=2x+1+√52x2−(3+√5)×2x+1−√52x2−(3−√5)Step 4
=((2x+1)+√5)((2x+1)−√5)((2x2−3)−√5)(((2x2−3)+√5))Step 5
=(2x+1)2−√52(2x2−3)2−√52Step 6
=4x2+4x+1−54x4−12x2+9−5Step 7
=4x2+4x−44x4−12x2+4Step 8
=x2+x−4x4−3x2+1
The coefficient is generated because the denominator of the 2 fractions in step 3 involves a fraction with denominator 2. So that 2 is multiplied in step 4 so the coefficient is generated.
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