on factor of x⁴+x²=1
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Answered by
26
Consider x4 + x2 + 1
= (x4 + 2x2 + 1) – x2
= [(x2)2 + 2x2 + 1] – x2
= [x2 + 1]2 – x2
It is in the form of (a2 – b2) = (a + b)(a – b)
Hence [x2 + 1]2 – x2 = [x2 + 1 + x] [x2 + 1 – x]
= (x4 + 2x2 + 1) – x2
= [(x2)2 + 2x2 + 1] – x2
= [x2 + 1]2 – x2
It is in the form of (a2 – b2) = (a + b)(a – b)
Hence [x2 + 1]2 – x2 = [x2 + 1 + x] [x2 + 1 – x]
Answered by
35
Step-by-step explanation:
x⁴+x²+1
=x⁴+2x²-x²+1
=(x⁴+2x²+1)-x²
=[(x²)²+2x²+(1)²]-x²
=(x²+1)²-x²
=(x²+1+x)(x²+1-x). Ans.
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