Question

Daca a+2c+3c=100 si 3a+2b+c=140, calculati (a+b+c)×(a-c).

Answer 1

a + 2b + 3c = 100
3a + 2b + c = 140
Adunam cele doua ecuatii si obtinem:
a + 2b + 3c + 3a + 2b + c = 100 +140
4a + 4b + 4c = 240
4(a + b + c) = 240
a + b + c = 60

Din a doua ecuatie o scadem pe prima si obtinem:
3a + 2b + c - (a + 2b + 3c) = 140-100
2a - 2c = 40
2(a - c) = 40
a -c = 20

Problema cere sa aflam (a + b + c) x (a - c) = 60 x 20 = 1200