Question

OMG PT A 3 OARA, EX 11!

Answer 1

Explicație pas cu pas:

x²+y²+z²=28

xy+yz+zx=22 =>2xy+2yz+2zx=44

=>

x²+y²+z²+2xy+2yz+2xz=72 => (x+y+z)²=72 dar x+z=y =>

(y+y)²=72 => (2y)²=72 =>4y²=72 =>y²=18 =>

y=3V2

Ca solutie avem si y = -3V2 dar ne spune ca x,y,z€R+

x+z=3V2

x²+y²+z²=28 => x²+z²+18=28=>x²+z²=10

xy+xz+yz=22 => y(x+z)+xz=22=>3V2*3V2+xz=22=>

18+xz=22=>xz=4=>2xz=8

x²+z²-2xz=(x-z)²=2 => x-z= V2 sau x-z = -V2

x+z=3V2

x-z = -V2

=>2x=2V2 =>x=V2=>z=2V2

x+z=3V2

x-z=V2 =>2x=4V2 =>x=2V2=>z=V2