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प्रश्न
Factorize: x4 + 1. (Hint: Try completing the square)
योग
उत्तर
The given equation is x4 + 1
x4 + 1 = (x2)2 + 12
= (x2 + 1)2 – 2 (x2) .....(1)
[a2 + b2 = (a + b)2 – 2ab]
= `(x^2 + 1)^2 – (sqrt(2)x)^2`
= `(x^2 + 1 + sqrt(2)x) (x^2 + 1 – sqrt2x)`
x4 + 1 = `(x^2 + 2x + 1) (x^2 – sqrt(2)x + 1)`
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