Question

Daca a,b,c sunt nr astfel incat a×b=0,06 ; b×c=0,12 si c×a=0,08,calculati suma a+b+c

Answer 1

[tex]a*b=0,06\\ b*c=0,12\\ c*a=0,08\\ a+b+c=?\\\\ a= \frac{0,06}{b} \\ b*c=12\\ \frac{0,06}{b} *c=0,08\\ 0,06c* \frac{c}{0,12} =0,08\\ 0,06 c^2=0,08*0,12\\ 0,06c^2=0,0096\\ c^2=0,0096:0,06\\ c^2=0,16\\ \bold{c= \sqrt{0,16} =0,4}\\\\ [/tex]

[tex]b= \frac{0,12}{c} \\\\ b= \frac{ \frac{0,06}{0,12} }{c} *c=0,08\\ b= \frac{0,12}{0,4} \\ \bold{b=0,3}\\\\ a= \frac{0,06}{0,3} \\ \bold{a=0,2}\\\\\\ a+b+c=0,2+0,3+0,4\\ \bold{a+b+c=0,9}[/tex]

Answer 2

a·b=0,06
⇒b=6/100/a⇒b=6/100·1/a⇒b=6/100a;
⇒b=3/50a;
c·a=0,08
⇒c=8/100/a⇒c=8/100·1/a⇒c=8/100a;
⇒c=4/50a⇒c=2/25a;
⇒b·c=12/100;
⇒3/50a·2/25a=12/100
⇒3/25a·1/25a=12/100
⇒3/25a·25a=12/100
⇒3/25·25·a²=12/100
⇒3/625·a²=12/100
⇒a²·625=3/12/100
⇒a²·625=3·100/12
⇒a²·625=100/4
⇒a²·625=25
⇒a²=25/625
⇒a²=0,04
⇒a²=0,2²⇒a=0,2;
⇒b=3/50a
⇒b=3/50·2/10
⇒b=3/50·1/5
⇒b=3/50/5
⇒b=3·5/50
⇒b=3/10;⇒b=0,3;
⇒c=2/25a
⇒c=2/25·2/10
⇒c=2/25·1/5
⇒c=2/25/5
⇒c=2·5/25
⇒c=2/5⇒c=0,4;⇒a+b+c=0,2+0,3+0,4⇒0,5+0,4⇒0,9;