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Răspunsuri la întrebare
Răspuns:
Explicație pas cu pas:
a) 3¹⁸ + 3¹⁷ = 3¹⁷ x ( 3 + 1) = 3¹⁷ x 4
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b) 2²⁹ + 2²⁷ - 2²⁶ = 9 x 4¹³
2²⁹ + 2²⁷ - 2²⁶ = 4¹³ x 9
= 2²⁶ x ( 2³ + 2² - 1 ) =
= 2²ˣ¹³ x ( 8 + 2 - 1 ) =
= ( 2²)¹³ x 9 =
= 4¹³x 9
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c)
5²⁶ + 5²⁵ - 15²⁴ : 3²⁴ = 25¹² x 29
= 5²⁶ + 5²⁵ - ( 15 : 3 )²⁴ =
= 5²⁶ + 5²⁵ - 5²⁴ =
= 5²⁴ x ( 5² + 5 - 1 ) =
= 5²⁴ x ( 25 + 5 - 1 ) =
= 5²⁴ x 29 =
= ( 5²)¹² x 29 =
= 25¹² x 29 c.c.t.d
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d)
49¹¹ : 7¹¹ + 7¹³ : 7 = (49:7)¹¹ + 7⁽¹³⁻¹⁾ = 7¹¹ + 7¹² = 7¹¹ x ( 1 + 7) = 7¹¹ x 8
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e)
7 x 4²³ - 9 x 4²² = 4²² x ( 7 x 4 - 9 ) = 4²² x ( 28 - 9) = 4²² x 19
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f)
3 x 6²⁰⁰⁸ - 2²⁰⁰⁷ x 3²⁰⁰⁷ - 5 x 6²⁰⁰⁶ =
= 3 x 6²⁰⁰⁸ - ( 2 x 3 )²⁰⁰⁷ - 5 x 6²⁰⁰⁶ =
= 6²⁰⁰⁶ x ( 3 x 6² - 6 - 5 ) =
= 6²⁰⁰⁶ x ( 3 x 36 - 11 ) =
= 6²⁰⁰⁶ x (108 - 11 ) =
= 6²⁰⁰⁶ x 97 -> c.c.t.d.