Question

Determinati numerele x, y, z, stiind ca x/3 =y/5=z/9


x²+y²+z²=1035​

Answer 1

Explicație pas cu pas:

(x,y,z) D.P (3,5,9)=>

=>x/3=y/5=z/9=k

"k"-raport de proporționalitatea.

x/3=k=>x=3k

y/5=>y=5k

z/9=k=>z=9k

x²+y²+z²=1035=>(3k)²+(5k)²+(9k)²=1035=>9k²+25k²+81k²=1035=>34k²+81k²=1035=>115k²=1035=>k²=1035÷115=>k²=9=>k=√9=3=>k=3

x=3k=3×3=9=>x=9

y=5k=5×3=15=>y=15

z=9×3=27=>z=27

Baftă!