Question

Clasa a 6.
Aflați cifra x,știind că xxx(x-1)=(x-1)la puterea x-2.
Vă rog mult!​

Answer 1

xxx(x-1)=(x-1)^(x-2)

1000x+100x+10x+x-1=(x-1)^(x-2)

1111x -1=(x-1)^(x-2)

x∈{1;2;3…;9}

1110≤1111x -1≤9998

(x-1)^(x-2)> 1111-1=1110

(6-1)^(6-2)=5⁴=625 => x>6;

x=7=> 6⁵=7776

7777-1=6⁵

pentru x>7=> 7⁸>9998

Deci, x=7.