Question

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Analyze the product of

x⁴ + x² +1

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Answer 1

Answer:

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Step-by-step explanation:

Easy!  Complete the squares to get:

x⁴ + x² + (½)² = 1 + (½)²

(x² + ½)² = 1 + ¼

(x² + ½)² = 3/4

Then, by square root property...

√(x² + ½)² = ±√(3/4)

x² + ¼ = ±√(3)/2

Finally...

x² = -¼ ± √(3)/2

x² = -¼ ± 2√(3)/4

x² = (-1 ± 2√3)/4

x = ±√((-1 ± 2√3)/4)

x = ±√(-1 ± 2√3)/2

I hope this helps!

Answer 2

Step-by-step explanation:

x⁴+x²+1.

=x⁴+2x²- x²+1.

=(x⁴+2x²+1)-x².

=[(x²)²+2x²+(1)²]-x².

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