Question

Vă rog din suflet! Măcar a)
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Answer 1

Răspuns

Explicație pas cu pas:

a + b = 12

ab = 24

(a + b)^2 = a^2 + 2ab + b^2

a^2 + b^2 = (a + b)^2 - 2ab = 144 - 48 = 96

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( a + b)^3 = a^3 + b^3 + 3a^2b + 3ab^2 =  a^3 + b^3 + 3ab (a + b)

a^3 + b^3  = ( a + b)^3 - 3ab (a + b) = 12^3 + 3*24*12 = 2592

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(a^2 + b^2)^2 = a^4 + b^4 + 2a^2b^2 = a^4 + b^4  + 2(ab)^2

a^4 + b^4  = (a^2 + b^2)^2 -  2(ab)^2 = 96^2 - 2*24^2 = 8064

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(a^3 + b^3)^2 = a^6 + b^6 + 2(ab)^3

a^6 + b^6 = (a^3 + b^3)^2 - 2(ab)^3 = 2592^2 - 2*24^3 = 6690816

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a + b = 12

ab = 24

(a + b)/ab = 12/24

1/b + 1/a = 1/2

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(1/a + 1/b)^2 = 1/a^2 + 1/b^2 + 2/ab

1/a^2 + 1/b^2  = (1/a + 1/b)^2 - 2/ab = 1/4 - 2/24 = 1/4 - 1/12 = 3/12 - 1/12 = 2/12 = 1/6

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(1/a^2 + 1/b^2)^2 = 1/a^4 + 1/b^4 + 2/(ab)^2

1/a^4 + 1/b^4 = (1/a^2 + 1/b^2)^2  - 2/(ab)^2 = 1/36 - 2/24^2 = 1/36 - 1/576 = 16/576 - 1/576 = 15/576 = 5/192

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(1/a + 1/b)^3 = 1/a^3 + 1/b^3 + 3/a^2b + 3/ab^2

3/a^2b + 3/ab^2 = 3b/a^2b^2 + 3a/a^2b^2  = 3(a + b)/(ab)^2

1/a^3 + 1/b^3 = (1/a + 1/b)^3 - 3(a + b)/(ab)^2 = 1/8 -36/24^2 = 1/8 - 36/576 = 72/576 - 36/576 = 36/576 = 9/144 = 1/16