Question

Cum rezolv exercitile astea ? :)
Ajutatima
a)$x^{2}$=1+3+5+...101
b)34+15(x+3)=(-13$)^{2}$
c)$\frac{2(x+2)}{x-1} - \frac{x+1}{x-2}$

Answer 1

a)x²=1+3+5+...101= (1+2+3+...+101)-(2+4+....100)=
=101×(101+1)/2-2(1+2+3...+50)=101×51-2×50×(50+1)/2=101×51-50×51=
=51(101-51)=51²
x²=51²
x=51
 b)34+15(x+3)=(-13)²
34+15x+45=169
15x=169-45-34
15x=90
x=90/15
x=6

c) 2(x+2)/(x-1)-(x+1)/(x-2) = [2(x+2)(x-2)-(x+1)(x-1)]/(x-1)(x-2) =
=[2(x²-4)-(x²-1)]/(x-1)(x-2) = (2x²-8-x²+1)/(x-1)(x-2) =
=(x²-7)/(x-1)(x-2)=
=(x²-7)/(x²-3x+2)