Question

x+1/x=2; x^2+1/x^2=2
$x + \frac{1}{x} = 2$
Demonstrați :
${x}^{2} + \frac{1}{ {x}^{2} } = 2$
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Answer 1

x+ 1/x=2 => x²+2x·1/x+1/x²=4

x²+2+1/x²=4  

=> x²+1/x²=2

Answer 2

Răspuns:

Explicație pas cu pas:

x + 1/x = 2   → ridic la patrat relatia

( x + 1/x)² = 2²

->  aplic formula ( a + b)² = a² + 2ab + b², unde a = 1  si b = 1/x

x² + 2 × x × 1/x + (1/x)² = 4

x² + 2 × (x/x) + 1/x² = 4

x² + 2 × 1 + 1/x² = 4

x² + 1/x² = 4 - 2

x² + 1/x² = 2 → ceea ce trebuia demonstrat