Question

calculati suma a patrat +b patrat+c patrat stiind ca a.b.c sunt cifre si ca : a,b +b,c+c,a =132/5,iar cifrele sunt distincte.

Answer 1

a,b=ab/10=10a+b/10
b,c=bc/10=10b+c/10
c,a=ca/10=10c+a/10
=> a,b+b,c+c,a= 10a+b/10 + 10b+c/10 + +10c+a/10=132/5
<=> 5(10a+b+10b+c+10c+a)=132×10
<=> 50a+5b+50b+5c+50c+5a=1320
<=> 55a+55b+55c=1320
<=> 55(a+b+c)=1320
=> a+b+c=1320/55
=> a+b+c=24
a;b;c -> cifre
=> (acesta este singurul caz posibil)
a=7}
b=9}=> a^2+b^2+c^2= 7^2+9^2+8^2=
c=8}. =49+81+64
=194
Raspuns: a^2+b^2+c^2= 194

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