Question

heii ma ajutati cu doua exercitii
1) Se considera numerele reale x,ysi 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
2) Descompuneti in factori
a) x la puterea a 2a -y la puterea a 2 a
b) x la puterea a 2 a - 9
c) 4- a la puterea a 2 a
d) 9 y la putereaa 2a - 16 z la puterea a 2 a
e) 25 x la puterea a 2 a -9y la puterea a 2 a
f) a la puterea a 2 a -49 ATAT.... DAU 11 PUNCTE CA ATATEA MAI AM SIPLUS COROANA !!!1

Answer 1

$1a).xy+xz=10 \\ x=2 \\ xy+xz=10 \rightarrow x(y+z)=10 \rightarrow2(y+z)=10 \rightarrow \boxed{y+z=5} \\ b).x-y=4 \\ z=5 \\ xz-yz=z(x-y)=5*4=\boxed{20} \\ c).xy+yz=20 \\ y=5 \\ xy+yz=20 \rightarrow y(x+z)=20 \rightarrow 5(x+z)=20 \rightarrow \boxed{x+z=4} \\ d).xy-xz=24 \\ y-z=6 \\ xy-xz=24 \rightarrow x(y-z)=24 \rightarrow 6x=24 \rightarrow x= \frac{24}{6} \rightarrow \boxed{x=4}$
$2a).x^2-y^2=(x-y)(x+y) \\ b).x^2-9=(x-3)(x+3) \\ c).4-a^2=(2-a)(2+a) \\ d).9y^2-16z^2=(3y-4z)(3y+4z) \\ e).25x^2-9y^2=(5x-3y)(5x+3y) \\ f).a^2-49=(a-7)(a+7)$