Question

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E URGENT!!!
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Answer 1

2. 64,81,100,121,144,169,194

5. a) 5²×6+5²×9+5²×10

factor comun: 5²

5²(6+9+10)=5²×25=25×25=25²

b) 7³+7³×2+7³×2²=7³(1+2+4)=7³×7=7⁴=49²

c)2+2+2²+2³+2⁴+2⁵=2+2+4+8+16+32=64=8²

d)1+3+5+7+9=25=5²

e)8+2(1+2+3+4+5+6+7)=8+2×28=64=8²

8. a) 1000²-1000-999=1000×1000-1×1000-999=1000(1000-1)-999=1000×999-999=1000×999-1×999=999(1000-1)=999×999=999²

b)25+25+...25(25 de termeni)=25×25=25²

c)57+2×(1+2+3+...+56)=57+2×56×57/2

=57+56×57=57×1+56×57=57(1+56)=57×57=57²

d)101+(2+4+6+...+200)=101+2(1+2+3+...+100)=101+2×100×101/2=101+100×101=1×101+100×101=101(1+100)=101×101=101²

11.

a=5n+3

n=1, 5+3=8

n=2, 10+3=13

n=3, 15+3=18

n=4, 20+3=23

Nu exista patrate perfecte care se termina in 3 si in 8

b=5n+7

n=1, b=12

n=2, b=17

n=3, b=22

n=4, b=27

Nu exista patrate perfecte care se termina in 2 si in 7

c=5n+8

n=1, c=13

n=2, c=18

n=3, c=23

Acelasi caz ca si la a

d=5n+2

n=1, d=7

n=2, d=12

n=3, d=17

Acelasi caz ca si la b

15.

2¹⁹⁹⁹-2¹⁹⁹⁸-2¹⁹⁹⁷-2¹⁹⁹⁶=2¹⁹⁹⁶×2³-2¹⁹⁹⁶×2²-2¹⁹⁹⁶×2-2¹⁹⁹⁶=2¹⁹⁹⁶(2³-2²-2-1)=2¹⁹⁹⁶(8-4-2-1)=2¹⁹⁹⁶×1=2¹⁹⁹⁶=(2⁹⁹⁸)² - patrat perfect