Exercitiu 3 si 4 va rog

RΔspuns
ExplicaΘie pas cu pas:
3 / (β5 - β2) = 3(β5 + β2) / (β5 - β2)(β5 + β2) = 3(β5 + β2) / (5 - 2) = β5 + β2
6/(β10 + 1) = 6(β10 - 1) / (β10 + 1)(β10 - 1) = 6(β10 - 1) /(10 - 1) = 6(β10 - 1) /9 = 2(β10 - 1) /3
β10 / (2β5 - β10) = β10 (2β5 + β10) / (2β5 - β10)(2β5 + β10) = β10 (2β5 + β10) / (20 - 10) = β10 (2β5 + β10) /10 = (β2*β5 * 2β5 + 10)/10 = (10β2 + 10) / 10 = β2 + 1
(β6 - β3) / (β6 - β3 - β2) = (β6 - β3)(β6 - β3 +β2) / (β6 - β3 - β2)(β6 - β3 +β2) = (β6 - β3)(β6 - β3 +β2) / (7 - 2β6β3) = (β6 - β3)(β6 - β3 +β2) / (7 - 6β2) = (β6 - β3)(β6 - β3 +β2)(7 + 6β2) / (7 - 6β2)(7 + 6β2) = (β6 - β3)(β6 - β3 +β2)(7 + 6β2) /(49 - 72) = (β6 - β3)(β6 - β3 +β2)(7 + 6β2) /23
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a + b = 3β6
ab = 12
(a + b)^2 = a^2 + b^2 + 2ab
a^2 + b^2 = (a + b)^2 -2ab = (3β6)^2 - 24 = 54 - 24 = 30