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Soluzione del esercizio 79 di Colori della Matematica - Edizione Blu, Vol. 1
Esercizi svolti per il libro Colori della Matematica - Edizione Blu, Vol. 1
Capitolo
Scegli il capitolo
Unità 1 - Numeri naturali e numeri interi
Unità 6 - Polinomi
Unità 8 - Equazioni di primo grado numeriche intere
Unità 17 - Dalla congruenza alla misura
Unità 20 - Quadrilateri
Esercizio
Scegli l'esercizio
73
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90
Soluzione
(
−
0.2
x
+
0.3
y
−
0.5
)
+
(
2
5
x
+
3
2
y
−
1
2
)
(-0.2x+0.3y-0.5) + (\dfrac{2}{5}x+\dfrac{3}{2}y-\dfrac{1}{2})
(
−
0.2
x
+
0.3
y
−
0.5
)
+
(
5
2
x
+
2
3
y
−
2
1
)
=
=
=
(
−
1
5
x
+
3
10
y
−
1
2
)
+
(
2
5
x
+
3
2
y
−
1
2
)
(-\dfrac{1}{5}x+\dfrac{3}{10}y-\dfrac{1}{2})+(\dfrac{2}{5}x+\dfrac{3}{2}y-\dfrac{1}{2})
(
−
5
1
x
+
10
3
y
−
2
1
)
+
(
5
2
x
+
2
3
y
−
2
1
)
=
=
=
−
1
5
x
+
3
10
y
−
1
2
+
2
5
x
+
3
2
y
−
1
2
-\dfrac{1}{5}x+\dfrac{3}{10}y-\dfrac{1}{2}+\dfrac{2}{5}x+\dfrac{3}{2}y-\dfrac{1}{2}
−
5
1
x
+
10
3
y
−
2
1
+
5
2
x
+
2
3
y
−
2
1
=
=
=
(
2
5
x
−
1
5
x
)
(\dfrac{2}{5}x-\dfrac{1}{5}x)
(
5
2
x
−
5
1
x
)
+
+
+
(
3
10
y
+
3
2
y
)
(\dfrac{3}{10}y+\dfrac{3}{2}y)
(
10
3
y
+
2
3
y
)
+
+
+
(
−
1
2
−
1
2
)
(-\dfrac{1}{2}-\dfrac{1}{2})
(
−
2
1
−
2
1
)
=
=
=
1
5
x
+
3
+
15
10
y
+
(
−
2
2
)
\dfrac{1}{5}x+\dfrac{3+15}{10}y+(-\dfrac{2}{2})
5
1
x
+
10
3
+
15
y
+
(
−
2
2
)
=
=
=
1
5
x
+
18
10
y
+
(
−
1
)
\dfrac{1}{5}x+\dfrac{\cancel{18}}{\cancel{10}}y+(-1)
5
1
x
+
10
18
y
+
(
−
1
)
=
=
=
1
5
x
+
9
5
y
−
1
\dfrac{1}{5}x+\dfrac{9}{5}y-1
5
1
x
+
5
9
y
−
1
(
−
0.2
x
+
0.3
y
−
0.5
)
−
(
2
5
x
+
3
2
y
−
1
2
)
(-0.2x+0.3y-0.5)-(\dfrac{2}{5}x+\dfrac{3}{2}y-\dfrac{1}{2})
(
−
0.2
x
+
0.3
y
−
0.5
)
−
(
5
2
x
+
2
3
y
−
2
1
)
=
=
=
(
−
1
5
x
+
3
10
y
−
1
2
)
−
(
2
5
x
+
3
2
y
−
1
2
)
(-\dfrac{1}{5}x+\dfrac{3}{10}y-\dfrac{1}{2})-(\dfrac{2}{5}x+\dfrac{3}{2}y-\dfrac{1}{2})
(
−
5
1
x
+
10
3
y
−
2
1
)
−
(
5
2
x
+
2
3
y
−
2
1
)
=
=
=
−
1
5
x
+
3
10
y
−
1
2
−
2
5
x
−
3
2
y
+
1
2
-\dfrac{1}{5}x+\dfrac{3}{10}y-\dfrac{1}{2}-\dfrac{2}{5}x-\dfrac{3}{2}y+\dfrac{1}{2}
−
5
1
x
+
10
3
y
−
2
1
−
5
2
x
−
2
3
y
+
2
1
=
=
=
(
−
1
5
x
−
2
5
x
)
(-\dfrac{1}{5}x-\dfrac{2}{5}x)
(
−
5
1
x
−
5
2
x
)
+
+
+
(
3
10
y
−
3
2
y
)
(\dfrac{3}{10}y-\dfrac{3}{2}y)
(
10
3
y
−
2
3
y
)
+
+
+
(
1
2
−
1
2
)
(\dfrac{1}{2}-\dfrac{1}{2})
(
2
1
−
2
1
)
=
=
=
−
3
5
x
+
3
−
15
10
y
-\dfrac{3}{5}x+\dfrac{3-15}{10}y
−
5
3
x
+
10
3
−
15
y
=
=
=
−
3
5
x
+
(
−
12
10
y
)
-\dfrac{3}{5}x+(-\dfrac{\cancel{12}}{\cancel{10}}y)
−
5
3
x
+
(
−
10
12
y
)
=
=
=
−
3
5
x
−
6
5
y
-\dfrac{3}{5}x-\dfrac{6}{5}y
−
5
3
x
−
5
6
y