Values from x plus its reciprocal
Values from x plus its reciprocal
IP 2
8 marks
It is given that \(x+\dfrac{1}{x}=5\), where \(x\ne0\).
- Find the value of \(x^2+\dfrac{1}{x^2}\).[2]
- Find the value of \(\left(x-\dfrac{1}{x}\right)^2\).[2]
- Show that \(x^4+\dfrac{1}{x^4}=527\).[2]
- Explain why there is no real number \(x\) for which \(x+\dfrac{1}{x}=1\).[2]
Solution:
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Answer:(a) \(23\) (b) \(21\) (c) Shown (d) It would give \(\left(x-\dfrac{1}{x}\right)^2=-3<0\)
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