Question

a+b=5
a*b=2
Calculati a/b+b/a
As dori raspuns complet ,Multumesc!
Scuzati materia !

Answer 1

Aducem la numitor comun: a/b + b/a= (a² + b²)/a*b= [(a+b)²-2•a•b]/(a•b)=(5²- 2•2)/2=21/2=10,5.

Answer 2

$\frac{a}{b}+ \frac{b}{a}= \frac{a^2+b^2}{ab}. \\ \\ a+b=5 \\ \\ (a+b)^2=25 \\ \\ a^2+2ab+b^2=25 \\ \\ a^2+2 \cdot 2+b^2=25 \\ \\ a^2+4+b^2=25 \\ \\ a^2+b^2=21$

$\frac{a}{b}+ \frac{b}{a}= \frac{a^2+b^2}{ab}= \frac{21}{2}.$