Question

1. Calculati media geometrica a numerelor $a= \sqrt{81} -3 \sqrt{3} + \sqrt{27}$  si $b=|2- \sqrt{3} |+ \frac{1}{2- \sqrt{3} } .$

2. Se considera expresia $E(x)=( \frac{2x-8}{ x^{2} -8x+15} - \frac{1}{x-3} ): \frac{1}{ x^{2} -25}$ . Aratati ca E(x)=x+5.

Answer 1

1. √81=9
√27=3√3

a=9-3√3+3√3
a=9

1/ (2-√3)  rationalizam si obtinem  (2-√3)/ 4-3=  (2+√3)/1=  2+√3

b=|2-√3| +2-√3
b= -2 +√3 + 2 +√3
b=2√3

mg=√ab= √9*2√3=√18√3=3√6

2.x²-8x+15= x²-3x-5x+15= x(x-3)-5(x-3)= (x-3)(x-5)
x²-25=(x-5)(x+5)

E(x)= [(2x-8)/(x-3)(x-5) - 1/ (x-3) ]  : 1/ (x-5)(x+5)  aducem la acelasi numitor in paranteza

(2x-8-x+5)/(x-3)(x-5) * (x-5)(x+5)/1=

=(x-3)/ (x-3) *  (x+5)=

=1 * (x+5)= x+5