Question

Se dau proportiile: $\frac{a}{2}= \frac{b}{3}$ si $\frac{b}{4}= \frac{c}{5}$

1)Sa se determine k si p astfel incat sa avem $\frac{a}{8}= \frac{b}{k}= \frac{c}{p}$

2)Daca k=12 si p=15 sa se determine a,b si c stiind ca:
b)ab+bc=69
c)a²+b²+c²=433

Answer 1

1) a/2=b/3 impartim cu 4
a/8=b/12
b/4=c/5 impartim  3
b/12=c/15
din a/8=b/k=c/p
rezulta k=12 si p=15
2) a)
ab+bc=69
a/8=b/12; a=2b/3
b/12=c/15; c=5b/4
inlocuim
(2b/3)·b+b·(5b/4)=69 aducem la acelasi numitor si adunam
b²·23/12=69
DACA a,b,c ∈R avem solutiile de mai jos
b=+-6
a=+-4
c=+-15/2
b) a²+b²+c²=433
inlocuim
4b²/9+b²+25b²/25=433
aducem la acelasi numitor si adunam
(64+144+225)b²/144=433
433b²/144=433
b=+-12
a=+-8
c=+-15