Question

Ajutați-mă vă rooog!!!! ​

Answer 1

2(5^d+2•abc)=2^c+2009

2(5^d+2•abc) este par; 2009 este impar => 2^c este impar

=> c=0; 2⁰=1

2(5^d+2•abc)=2010     /:2

5^d+2•abc=1005

=> d∈{0;1;2;3;4}

d=0=> 5⁰+2•abc=1005

2•abc=1004

abc=502

d=1=> 5¹+2•abc=1005

2•abc=1000

abc=500

d=2=> 5²+2•abc=1005

2•abc=980

abc=490

d=3=> 5³+2•abc=1005

2•abc=1005-125=880

abc=880:2

abc=440

d=4=> 5⁴+2•abc=1005

2•abc=1005-625=380

abc=380:2

abc=190

abc∈{190; 440; 490; 500; 502}