Question

if x -1/x =√3 tgen find the value of xsquare + ysquare

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Answer 1

Answer:

The question could be wrong. I think we need to find $x^{2} +\frac{1}{x^{2}}$ instead of $x^{2} +y^{2} = ?$, because here is no "y" given in the question.

GIVEN:

$x-\frac{1}{x} =\sqrt{3}$

RTF:

$x^{2} +\frac{1}{x^{2}}$

SOLUTION:

$x-\frac{1}{x} =\sqrt{3}$

• Square on both sides.

$(x-\frac{1}{x})^{2} =(\sqrt{3})^{2}$

• Simplify $(x-\frac{1}{x})^{2}$ and $(\sqrt{3})^{2}$.

$(x^{2} +(\frac{1}{x})^{2} +2\times x \times\frac{1}{x} ) =(\sqrt{3})\times(\sqrt{3})$

$x^{2} +\frac{1}{x^{2}} +2 =3$

• Transpose 2 to the RHS.

$x^{2} +\frac{1}{x^{2} } =3-2$

$x^{2} +\frac{1}{x^{2}} =1$

HOPE THIS HELPS :D

Answer 2

Answer:

Write your Q clearer first. You didn't mention about y variable.

So, now we can evaluate x² or x²+ 1/x²

Step-by-step explanation:

x- 1/x =√3

x²- 1=√3

x²=1+√3

•••

x- 1/x =√3

(x- 1/x)²=(√3)² [Squaring]

x²+ 1/x² –2.x.1/x=3 [x²+y²–2xy]

x²+ 1/x²= 3–2= 1