Question

Forma cea mai simpla a expresiei E(x)=[(x+5/x-5)^2+1+2x+10/x-5] *x-5/4x + 2 .
Va rog repede repede repede

Answer 1

[(x+5/x-5)²+1+2x+10/(x-5)]*(x-5)/(4x+2)=
[(x+5)²+(x-5)²+2x(x-5)²+10(x-5)]/(x-5)²=
[(25+10x+x²+25-10x+x²+2(x²-10x+25)x+10(x-5))*(x-5)]/[2(2x+1)(x-5)²]=
[(25+10x+x²+25-10x+x²+2x³-20x²+50x+10(x-5))*(x-5)]/[2(2x+1)(x-5)²]=
[(10x-50+2x³+x²+x²-20x²+50x+10x-10x+25+25))*(x-5)]/[2(2x+1)(x-5)²]=
[(2x³-18x²+60x+(25+25-50))*(x-5)]/[2(2x+1)(x-5)²]=
[(2x(x²-9x+30))*(x-5)]/[2(2x+1)(x-5)²]=
[x(x²-9x+30)(x-5)]/[(x-5)²(2x+1)]=
[x(x²-9x+30)(x-5)⁻¹]/(2x+1)=
(x³-9x²+30x)/[(x-5)(2x+1)]  - Forma cea mai simpla a expresiei

Pentru a afla "x" egalam cu zero
(x³-9x²+30x)/[(x-5)(2x+1)]=0
x(x²-9x+30)=0
x=0
x²-9x+30=0
x²-9x=-30
x-9x+81/4=-39/4
(x-9/2)²=-39/4
(x-9/2)²≥0 si -39/4>0
x=0