Answer:
x² + [tex]\frac{1}{x^2}[/tex] = 5
Step-by-step explanation:
using the identity
(a - b)² = a² + b² - 2ab , then given
(x - [tex]\frac{1}{x}[/tex] ) = [tex]\sqrt{3}[/tex] ( square both sides )
(x - [tex]\frac{1}{x}[/tex] )² = ([tex]\sqrt{3}[/tex] )² , that is using the above identity
x² + [tex]\frac{1}{x^2}[/tex] - 2(x × [tex]\frac{1}{x}[/tex] ) = 3
x² + [tex]\frac{1}{x^2}[/tex] - 2(1) = 3
x² + [tex]\frac{1}{x^2}[/tex] - 2 = 3 ( add 2 to both sides )
x² + [tex]\frac{1}{x^2}[/tex] = 5
[tex]\displaystyle\\Answer:\ x^2+\frac{1}{x^2}=5[/tex]
Step-by-step explanation:
[tex]\displaystyle\\(x-\frac{1}{x} )=\sqrt{3} \\[/tex]
Let's square both parts of the equation:
[tex]\displaystyle\\(x-\frac{1}{x} )^2=(\sqrt{3})^2 \\(x)^2-2*x*\frac{1}{x} +(\frac{1}{x})^2 =3\\x^2-2*1+\frac{1}{x^2}=3\\ x^2-2+\frac{1}{x^2}+2 =3+2\\x^2+\frac{1}{x^2}=5[/tex]
