Question

Utilizând factorul comun, arătaţi că: 318 + 317 = 4.317; 526 + 525 - 1524 : 324 = 29.2512; - b 229 +227 - 226 = 9.413; d 4911: 711 + 713 : 7 = 8.711, 13. 62008 - 22007. 32007 - 5. 62006 = 97.62006 e 7.423 - 9.422 = 19.422,VA ROOOOG DAU CORONA PLSSSSS AJUTATIMA​

Answer 1

Răspuns:

Explicație pas cu pas:

a)

3¹⁸ + 3¹⁷ = 4 x 3¹⁷

3¹⁷x3 + 3¹⁶x3 = 4 x 3¹⁷

3¹⁷ x ( 3+1) = 4 x 3¹⁷

3¹⁷ x 4 = 4 x 3¹⁷

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b) 2²⁹ + 2²⁷ - 2²⁶ = 9 x 4¹³

2²⁶ x 2³ + 2²⁶ x 2 - 2²⁶ x 1 =

- îl dau factor comun pe 2²⁶

= 2²⁶ x ( 2³ + 2 - 1 ) =

= 2²ˣ¹³ x ( 8+2-1) =

= (2²)¹³ x 9 =

= 4¹³ x 9   --- c.c.t.d.

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c) 5²⁶ + 5²⁵ - 15²⁴ : 3²⁴ = 29 x 25¹²

5²⁴x5² + 5²⁴x5 - (5x3)²⁴: 3²⁴ =

5²⁴x25 + 5²⁴ x 5 - 5²⁴x3²⁴:3²⁴ =

5²⁴ x ( 25 + 5 - 1 ) =

= 5²⁴ x 29 =

= 5²ˣ¹² x 29 =

= (5²)¹² x 29 =

= 25¹² x 29  -- c.c.t.d

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d) 49¹¹: 7¹¹ + 7¹³ : 7 = 8 x 7¹¹

(7²)¹¹ : 7¹¹ + 7⁽¹³⁻¹⁾ =

= 7²²⁻¹¹ + 7¹² =

= 7¹¹ + 7¹² =

= 7¹¹ x ( 1+7) =

= 7¹¹ x 8

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e) 7 x 4²³ - 9 x 4²² = 19 x 4²²

= 7 x 4 x 4²² - 9 x 4²² =

= 4²² x ( 28 - 9 ) =

= 4²² x 19

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f) 3x6²⁰⁰⁸  - 2²⁰⁰⁷ x 3²⁰⁰⁷ - 5 x 6²⁰⁰⁶ = 97 x 6²⁰⁰⁶

= 3x6²⁰⁰⁶ x 6² - (2x3)²⁰⁰⁷ - 5x6²⁰⁰⁶ =

= 6²⁰⁰⁶ x ( 3x36 - 6 - 5) =

= 6²⁰⁰⁶ x (108 - 11) =

= 6²⁰⁰⁶ x 97  -- ceea ce trebuia demonstrat