Question

If x square +1\x square =3,find the value of x+1/x

Answer 1

Answer:

$\large{\bold{2\sqrt2 \;\;,\;\;-2\sqrt2 }}$

Step-by-step explanation:

$FORMULA\\\\(a+b)^2=a^2+b^2+2ab\\\\Given\\\\x^2+\frac{1}{x^2}=3\\\\Consider\\\\(x+\frac{1}{x})^2\\\\=x^2+\frac{1}{x^2}+2\times x\times \frac{1}{x}\\\\=x^2+\frac{1}{x^2}+2\\\\=3+5\\\\=8\\\\=>(x+\frac{1}{x})^2=8\\\\Taking\;SQUARE\;root\\\\=>|x+\frac{1}{x}|=2\sqrt{2}\\\\If\;x>0\\\\=>x+\frac{1}{x}=2\sqrt2 \\\\If\;\;x<0\\\\=>x+\frac{1}{x}=-2\sqrt2$

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