Question

Daca
$x { }^{} + \frac{1}{x {}^{} } = 3$
si

$x - \frac{1}{x} = \sqrt{5}$
sa se calculeze......​

Answer 1

Răspuns:

Explicație pas cu pas:

a)

x² + 1/x² = ?

( x + 1/x)² = 3²

x² + 2 x/x + 1/x² = 9

x² + 1/x² = 9 - 2

x + 1/x² = 7

___________________

b)

x² - 1/x² = ( x - 1/x ) ( x + 1/x ) = 3 × √5 = 3√5

_____________________________________

c)

x³ - 1/x³ = ( x - 1/x ) ( x² + x/x + 1/x² ) = √5 × 8= 8√5

x² +x/x + 1/x² = (x²+1/x²) + 1 = 7+1=8