👤
Her1236go
Respondido

without determining the value of x, evaluate x² + ¹/x² if x - ¹/x = 5​

Resposta :

CrazyxDgo

We know [tex]x - \frac{1}{x} = 5[/tex] .

Notice that the x the question wants is squared, and also notice that when we multiply x and 1/x, they cancel out. So by squaring both sides of equations and manipulating it:

[tex](x - \frac{1}{x})^2 = 5^2\\\\(x^2 - 2 *x*(-\frac{1}{x}) + \frac{1}{x^2}) = 25\\\\x^2 + 2 +\frac{1}{x^2} = 25\\\\x^2 +\frac{1}{x^2} = 23[/tex]

Rafames1000go

If  [tex]x-\frac{1}{x}=5[/tex]

[tex]x^{2} +\frac{1}{x^{2} } =?[/tex]

[tex]x-\frac{1}{x}=5[/tex]

[tex](x-\frac{1}{x})^{2} =5^{2}[/tex]

[tex]x^{2} +2.x.(-\frac{1}{x}) +(-\frac{1}{x} )^{2} =25[/tex]

[tex]x^{2} -\frac{2x}{x} +\frac{1^{2} }{x^{2} } =25[/tex]

[tex]x^{2} -2+\frac{1 }{x^{2} } =25[/tex]

[tex]x^{2} +\frac{1 }{x^{2} } =25+2[/tex]

[tex]x^{2} +\frac{1 }{x^{2} } =27[/tex]

27

Go Schools: Outras perguntas