Bài 1: CHo a+5 /a-5=b+6/b-6.CHứng minh rằng a/b = 5/6
Bài 2: CHo( x+16)trên9=(y-25)trên16=(z+9)trên25và 2xngũ3 -1 = 15 .Tính x+y+z.
Bài 1: [TEX]\frac{a+5}{a-5}=\frac{b+6}{b-6}[/TEX]
\Leftrightarrow (a+5)(b-6) = (a-5)(b+6) \Leftrightarrow ab+5b-6a-30= ab-5b+6a-30 \Leftrightarrow 10b= 12a \Rightarrow [TEX]\frac{a}{b}=\frac{10}{12}=\frac{5}{6}[/TEX]
Bài 2: [TEX]2x^3-1= 15 \Rightarrow 2x^3=16 \Rightarrow x^3= 8 \Rightarrow x=2[/TEX]
[TEX]\frac{x+16}{9}=\frac{y-25}{16}=\frac{z+9}{25}[/TEX]
\Rightarrow [TEX]\frac{x+16}{9}=\frac{y-25}{16}=\frac{z+9}{25}=\frac{x+16+y-25+z+9}{9+16+25}=\frac{x+y+z}{50}[/TEX]
\Rightarrow [TEX]\frac{x+y+z}{50}=\frac{x+16}{9}=\frac{2+16}{9}=2 \Rightarrow x+y+z = 2.50 = 100[/TEX]