Question

4. Se considera numerele reale x,y,z
a) Daca xy + xz = 10 si x = 2, calculati y+z
b) Daca x - y = 4 si z = 5, calculati xz-yz
c) Daca xy + yz = 20 si y = 5, calculati x+z
d) Daca xy - xz = 24 si y - z = 6, calculati x

5. Descompuneti in factori :
a) x^2 - y^2
b) x^2 - 9
c) 4 - a^2
d) 9y^2 - 16z^2
e) 25x^2 - 9y^2
f) a^2b^2 - 49

Answer 1

a) Daca xy + xz = 10 si x = 2, calculati y+z
x(y+z)=10
2(y+z)=10
y+z=5

b) Daca x - y = 4 si z = 5, calculati xz-yz
 xz-yz=z(x-y)=5 *4=20

c) Daca xy + yz = 20 si y = 5, calculati x+z
xy + yz=20
y(x+z)=20
x+ z=20:5=4

d) Daca xy - xz = 24 si y - z = 6, calculati x
xy - xz = 24 
x(y-z)=24
y-z=24:6=4

5. Descompuneti in factori :
a) x² - y² =(x+y)(x-y)
b) x² - 9=(x+3)(x-3)
c) 4 - a²=(2+a)(2-a)
d) 9y² - 16z²=(3y+4z)(3y-4z)
e) 25x² - 9y²=(5x + 3y)(5x - 3y)
f) a²b² - 49=(ab +7)(ab-7)