Question

(Algebra) Onde estou errando?

Sendo x um número real, tal que x + 1/x = 3, obtenha os valores numericos de:
a) x^2 + 1/x^2

Se,
x + 1/x = 3
x^2/x = 3
x = 3

logo,
x^2 + 1/x^2
3^2 + 1/3^2
9 + 1/9
82/9

Answer 1

 Olá,

$x+\frac{1}{x}=3\\\\\\\left(x+\frac{1}{x}\right)^2=(3)^2\\\\\\x^2+2\cdot\,x\cdot\frac{1}{x}+\frac{1}{x^2}=9\\\\\\x^2+\frac{2x}{x}+\frac{1}{x^2}=9\\\\\\x^2+2+\frac{1}{x^2}=9\\\\\\x^2+\frac{1}{x^2}=9-2\\\\\\\boxed{x+\frac{1}{x^2}=7}$

Answer 2

$(x+\frac{1}{x})=3~\Rightarrow~(x+\frac{1}{x})^2=3^2$

$(x+\frac{1}{x})^2=x^2+2\cdot \not\ x\cdot\dfrac{1}{\not\ x}+\dfrac{1}{x^2}=9$

$x^2+\dfrac{1}{x^2}+2=9$

$x^2+\dfrac{1}{x^2}=7$