Question

1.Determinati numerele naturale de forma abc care verifica relatia abc-ab-c=207.
2.Determinati numerele reale nenule a si b, stiind ca (a+2b)(1 pe a+1 pe 2b)=4 si 2a+3b=$\sqrt{98}$

Answer 1

1
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abc-ab-c=207
100a+10b+c-10a-b-c=207
90a+9b=207
10a+b=23
b=3
a=2
c={0,1,2,3,4,5,6,7,8,9}
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numerele de forma abc   sunt:230,231,232,233,234,235,236,237,238,239

2.
(a+2b)(1/a+1/2b)=4
(a+2b)(2b+a)/2ab=4
(a+2b)²=8ab
a²+4ab+4b²=8ab
 a²-4ab+4b²=0
a-2b=0   
a=2b

2a+3b=√98
2a+3b=7√2 
2×2b+3b=7√2 
7b=7√2 
b=√2 
a=2√2