Question

X la adoua - (y-z) totul la adoua =42.
2x + 2y - 2z =12. Aflați x-y+z=?

Answer 1

Răspuns:

x²-(y-z)² = 42

[x-(y-z)][x+(y-z)] = 42

(x-y+z)(x+y-z) = 42 |·2

(x-y+z)(2x+2y-2z) = 84

(x-y+z)•12 = 84

x-y+z=84:12

x-y+z = 7

Answer 2

Răspuns:

7

Explicație pas cu pas:

x²-(y-z)²=42

Aplicam formula: a²-b²=(a-b)(a+b).

In cazul de fata a²=x² si b²=(y-z)².

[x-(y-z)][x+(y-z)]=42

(x-y+z)(x+y-z)=42

Din 2x+2y-2z=12, scoatem x+y-z.

2x+2y-2z=12

2(x+y-z)=12 => x+y-z=6.

Inlocuim in relatia (x-y+z)(x+y-z)=42 si scoatem x-y+z.

(x-y+z)*6=42

x-y+z=7