Răspuns:
1. a)-2x+3x-x=-3x+3x=0
b) (-2x²)²=4x⁴
c) -2x+4y+8z=2(-x+2y+4z)
d) E(x)=[tex]\frac{2}{x-2}[/tex] nu are sens daca este 0 ⇒
x-2≠0 ⇒ x≠2 ⇒ x∈R\{2}
2.a) [tex]\frac{x^{2}-10x+25}{x^{2}-25}=\frac{(x-5)^{2} }{(x-5)(x+5)} =\frac{x-5}{x+5}[/tex]
b) (x-3)(x+3)=x²-9
c) [tex](-\frac{x^{2} }{y^{4}}):(-\frac{x^{4}}{y^{2}})= \frac{x^{2} }{y^{4}}*\frac{y^{2}}{x^{4}}=\frac{1}{x^{2}y^{2} }[/tex]
d) E(x)=[tex]\frac{3-x}{2}[/tex]
[tex]E(\sqrt{2}+1)=\frac{3-\sqrt{2}-1}{2} =\frac{2-\sqrt{2}}{2}[/tex]
[tex]E(1-\sqrt{2})=\frac{3-1+\sqrt{2}}{2} =\frac{2+\sqrt{2}}{2}[/tex]
[tex]E(\sqrt{2}+1)+E(1-\sqrt{2})=\frac{2-\sqrt{2}}{2}+\frac{2+\sqrt{2}}{2}=2[/tex]
3. a) [tex]\frac{x}{x^{2}-x}=\frac{x}{x(x-1)}=\frac{1}{x-1}[/tex]
b) 2a=3b
[tex]\frac{2a+b}{12a-5b}=\frac{3b+b}{6*3b-5b}=\frac{4b}{13b} =\frac{4}{13}[/tex]
c) [tex](2x+1)^{2}-1= 2x(2x+3)-5[/tex]
[tex](2x+1)^{2}-2= 2x(2x+3)-5\\4x^{2} +4x+1-2=4x^{2} +6x-5\\4x^{2}-4x^{2}-1+5=6x-2x\\4=4x[/tex] ⇒ x=1
d) (x²+4x+3)(x-1)=(x²+2x-3)(x+1)
x³+3x²+3x-3=x³+3x²-2 ⇒ x=-1
Explicație pas cu pas:
