Question

sabe-se que
$\sqrt{x} + \frac{1}{ \sqrt{x} } = 2$
,calcule
$x - \frac{1}{ \sqrt{x} }$
.

Answer 1

√x + 1/√x = 2

√x.√x/√x = √x = √x²/√x = x/√x

x/√x +1/√x = x + 1/√x

x + 1/√x = 2

(2√x)² = (x + 1)²

4x = x² + 2x + 1

x² + 2x + 1 - 4x = 0

x² - 2x + 1 = 0

S = 2/1 = 2
P = 1/1 = 1

x = 1


√x = √1 = 1


1 - 1/1 = 1 - 1 = 0