Question

Factorise:- x4 +1/x4+1

Answer 1

Answer:

$(x^2+\frac{1}{x^2}+1)(x^2+\frac{1}{x^2}-1)$

Step-by-step explanation:

$Given\\\\x^4+\frac{1}{x^4}+1\\\\=(x^2)^2+(\frac{1}{x^2})^2+1\\\\=(x^2)^2+(\frac{1}{x^2})^2+2\times x^2\times\frac{1}{x^2}-1\\\\=((x^2)+(\frac{1}{x^2}))^2-1\\\\=(x^2+\frac{1}{x^2})^2-1^2\\\\=(x^2+\frac{1}{x^2}+1)(x^2+\frac{1}{x^2}-1)\\\\\bold{\large{=(x^2+\frac{1}{x^2}+1)(x^2+\frac{1}{x^2}-1)}}\\\\\\\\\large{\bold{FORMULAE}}\\\\\bold{\boxed{(a+b)^2=a^2+b^2+2ab}}\\\\\bold{\boxed{a^2-b^2=(a+b)(a-b)}}$

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