Răspuns:
x = 5; y = 2; z = 9
Explicație pas cu pas:
[tex]\overline {11,x9} - \overline {y,3z8} = \overline {z,1zy} \ \Big| \ (*1000)\\\overline {11x90} - \overline {y3z8} = \overline {z1zy}[/tex]
[tex]\begin{array}{ccccc}1&1&x&9&0\\&y&3&z&8\\-&-&-&-&-\\&z&1&z&y\end{array}[/tex]
=> y = 2
[tex]\begin{array}{ccccc}1&1&x&9&0\\&\red{\bf2}&3&z&8\\-&-&-&-&-\\&z&1&z&\red{\bf2}\end{array}[/tex]
z poate fi 4 sau 9
pentru z = 4:
[tex]\begin{array}{ccccc}1&1&x&9&0\\&\red{\bf2}&3&\red{\bf4}&8\\-&-&-&-&-\\&\red{\bf4}&1&\red{\bf4}&\red{\bf2}\end{array}[/tex]
=> imposibil
pentru z = 9:
[tex]\begin{array}{ccccc}1&1&x&9&0\\&\red{\bf2}&3&\red{\bf9}&8\\-&-&-&-&-\\&\red{\bf9}&1&\red{\bf9}&\red{\bf2}\end{array}[/tex]
=> x = 5
[tex]\begin{array}{ccccc}1&1&\red{\bf5}&9&0\\&\red{\bf2}&3&\red{\bf9}&8\\-&-&-&-&-\\&\red{\bf9}&1&\red{\bf9}&\red{\bf2}\end{array}[/tex]
=> 11,59 - 2,398 = 9,192
