Question

Calculati media geometrica si media aritmetica pentru numerele. EX.8

Answer 1

Răspuns:

Explicație pas cu pas:

a)

a = (√3 - 1)^2 = 3 - 2√3 + 1 = 4 - 2√3

b = 4 - 2√3

Ma = (a + b) : 2 = (4 - 2√3 + 4 - 2√3) : 2 = (8 - 4√3) : 2 = 4 - 2√3

a*b = (4 - 2√3)*(4 - 2√3) = (4 - 2√3)^2

Mg = √a*b = I4 - 2√3I = 4 - 2√3

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b)

a = (2√5 + √3)^2 = 20 + 4√15 + 9 = 29 + 4√15

b = (√3 - √20)^2 = (√3 - 2√5)^2 = 9 - 5√15 + 20 = 29 - 4√15

Ma = (29 + 4√15 + 29 - 4√15) : 2 = 58 : 2 = 29

a*b = (29 + 4√15)(29 - 4√15) = 841 - 240 = 601

Mg = √601

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c)

a = (2√3 + √5)^2 = 12 + 4√15 + 5 = 17 + 4√15

b = (√12 - √5)^2 = 12 - 2√60 + 5 = 17 - 4√15

Ma = (17 + 4√15 + 17 - 4√15) : 2 = 34 : 2 = 17

a*b = (17 + 4√15)(17 - 4√15) = 289 - 240 = 49

Mg = √49 = 7

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d)

a = (√2 + 1)^2 = 2 + 2√2 + 1 = 3 + 2√2

b = √(17 - 12√2) = √(9 - 12√2 + 8) = √(3 - 2√2)^2 = I3 - 2√2I = 3 - 2√2

Ma = (3 + 2√2 + 3 - 2√2) : 2 = 6 : 2 = 3

a*b = (3 + 2√2)(3 - 2√2) = 9 - 8 = 1

Mg = √1 = 1