Question

Numerele rationale a,b,c sunt d.p cu numerele 2, 3 si 4. Stiind ca 6a la a2a +b la la a2aa2a-2c la a2a=9 , determinati numerele a, b, c .

Answer 1

{a,b,c}dp{2,3,4}
a/2=b/3=c/4=k
a/2=k⇒a=2k
b/3=k⇒b=3k
c/4=k⇒c=4k
6a²+b²-2c²=9
6·4k²+9k²-2·16k²=9
24k²+9k²-12k²=9
21k²=9
k²=9/12
k=√9/12=3/2√3=3√3/6=√3/2
a=2k=2√3/2=√3
b=3k=3√3/2
c=4k=4√3/2=2√3