If x + 1/x=2 , find x^2 + 1/x^2 and x^4 + 1/x^4

Answers 2

Answer:

2, 2

Step-by-step explanation:

[tex]x + \frac{1}{x} =2\\(x + \frac{1}{x}x)^{2} =4\\{using (a+b)^2=a^2+b^2+2ab}\\x^2 + \frac{1}{x^2}+2=4\\x^2 + \frac{1}{x^2}=2\\\\(x^2 + \frac{1}{x^2})^2=4\\\\x^4+\frac{1}{x^4}+2=4\\\\x^4+\frac{1}{x^4}=2[/tex]

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