Question

Demonstrati ca x,y,z,t apartin {1,2,3,4} stiind ca x supra 5 + y supra 5 la patrat + z supra 5 la cub + t supra 5 la a patra = 0,4704??

Answer 1

x/5 + y/5² + z/5³ +t/5⁴= 0,4704
x/5+ y/25 +z/125 +t/625=0,4704
125x/625 + 25y/625 + 5z/625 + t/625 = 4704/10000
(125x+25y+5z+t) : 625 = 4704/10000
125x+25y+5z+t= 4704 * 625 : 10000= 4704 : 16=294
125x+25y+5z+t=294
daca x=2 ; y=1; z=3 si t=4 obtinem
125*2 + 25*1 + 5*3+ 4=294
250+25+15+4=294
250+40+4=294
294=294 (adevarat) ⇒ x,y,z,t ∈ {1,2,3,4}