Question

Ma puteti ajuta ????
Ex:
38, 39, 40, 41
Sau macar una din ele .
Ofer 25 puncte !!!

Answer 1

....................................

Answer 2

38.
    ____    ____
a) abab +baba=6666
1010a+101b+1010b+101a=6666
1111a+1111b=6666
1111(a+b)=6666
a+b=6
a={1,2,3,4,5}
b={5,4,3,2,1}            __  
numerele de forma ab ={15,24,33,42,51}


b)
a00a+b00a=4004
1001a+1000b+a=4004
1000a+a+1000b+a=4004
1000(a+b)+2a=4004
2a=4  a=2    
1000(a+b)=4000
a+b=4     b=4-2=2
numerele de forma ab ={22}

c)a1b+b1a=424
100a+10+b+100b+10+a=424
101a+101b=404
101(a+b)=404
a+b=4
a={1,2,3}
b={3,2,1}
numerele de forma ab ={13,22,31}

39.
ab+ba+aa+bb+a0+b0=160
10a+b+10b+a+11a+11b+10a+10b=160
32a+32b=160
32(a+b)=160
a+b=5
a={1,2,3,4}
b={4,3,2,1}
numerele de forma ab ={14,23,32,41}

41.2+4+6+....+abc=abc00
2=2×1
4=2×2
6=2×3
.........
abc=2×n
2+4+6+....+abc=2(1+2+3+...+n)=2n(n+1):2=n(n+1)
abc000=abc×100=2n×100=200n
n(n+1)=200n
n²+n-200n=0
n²-199n=0
n(n-199)=0
n₁=0   
n₂=199

Verificare:
n=0
abc=0⇒nu e numar de 3 cifre deci nu este solutie
n=199
abc=2n=2×199=398
2+4+6+...+398=2(199*200)/2=39800
abc00=398×100=39800
deci numarul de forma abc ={398}