Question

1.Calculati: a^2, a^3, a^2+1,5a^2+1 daca: a)a=10, b)a=3, c)a=12.
2.Calculati: 5^0^2+5^2^0+5^1^2+2^2^1.
3.Aratati ca n=2013*2012+2013*2+2014 este patrat perfect

Answer 1

Răspuns:

Explicație pas cu pas:

1)  a)   a = 10

a² = 10² = 10 × 10 = 100

a³ = 10³ = 1000

a² + 1 = 10² + 1 = 100 + 1 = 101

5 a² + 1 = 5 × 10² + 1 = 5 x 100 + 1 = 500 + 1 = 501

b)   a = 3

3² = 9;  

3³ = 3 x 3 x 3 = 27

3² + 1 = 9 + 1 = 10

5 × 3² + 1 = 5 × 9 + 1 = 45 + 1 = 46

c) a = 12

12² = 12 × 12 = 144

12³ = 144 × 12 = 1 728

12² + 1 = 144 + 1 = 145

5 × 12² + 1 = 5 × 144 + 1 = 720 + 1 = 721

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2).

5^0^2 = 5⁰ ( 0² = 0)  ->  se ridica exponentul mai intai, apoi baza

5^2^0 = 5¹  ( 2⁰ = 1 )

2^2^1 = 2²   ( 2¹ = 2 )

5⁰ + 5¹ + 2² = 1 + 5 + 4 = 10

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3).

n = 2013 × 2012 + 2013 × 2 + 2014

n = 2013 × ( 2012 + 2 ) + 2014

n = 2013 × 2014 + 2014

n = 2014 × ( 2013 + 1 )

n = 2014 × 2014

n = 2014² → patrat perfect