Question

am nevoie urgent, dau coroana
$\frac{ \sqrt{3} - 1 }{ \sqrt{3} } + \frac{ \sqrt{5} - \sqrt{3} }{ \sqrt{15} } + \frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{35} } + \frac{ \sqrt{9} - \sqrt{7} }{ \sqrt{63} }$
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Answer 1

Răspuns:

2/3

Explicație pas cu pas:

(√3-1)/√3 + (√5-√3)/√15 + (√7-√5)/√35+(√9-√7)/√63 =

= √3·(√3-1)/3 + √15· (√5-√3)/15 + √35·(√7-√5)/35+√63·(√9-√7)/63 =

= ¹⁰⁵⁾(3-√3)/3 + ²¹⁾(5√3-3√5)/15 + ⁹⁾(7√5-5√7)/35 + ⁵⁾(9√7-7√9)/63 =

= (315-105√3+105√3-63√5+63√5-45√7+45√7-105)/315 =

= (315-105)/315 = 210/315⁽⁷ = 30/45⁽⁵ = 6/9⁽³ = 2/3