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lesantik [10]
2 years ago
9

Factorise x ^ 4 + 1/x ^ 4 - 3​

Mathematics
1 answer:
kondaur [170]2 years ago
7 0

Answer:

Step-by-step explanation:

Add 1 and subtract 1, so that the expression won't change.

x^{4}+\frac{1}{x^{4}}-3=x^{4}+\frac{1}{x^{4}}-3 +1 - 1\\\\=x^{4}+\frac{1}{x^{4}} - 2 + 1\\\\= (x^{2})^{2} + (\frac{1}{x^{2}})^{2}- 2 *x^{2}*\frac{1}{x^{2}} - 1\\\\

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

(a² - b²) = (a+b)(a - b)

Here a = x² - (1/x²)  and b = 1

= [ (x^{2}-\frac{1}{x^{2}})+ 1 ] [ (x^{2} -\frac{1}{x^{2}} - 1 ]

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