Câu 13:
1:
a: \(2x^2+2x=2x\cdot x+2x\cdot1=2x\left(x+1\right)\)
b: \(9x^2-4y^2\)
\(=\left(3x\right)^2-\left(2y\right)^2\)
=(3x-2y)(3x+2y)
2:
\(\dfrac{xy+2x+1}{xy+x+y+1}+\dfrac{yz+2y+1}{yz+y+z+1}+\dfrac{zx+2z+1}{zx+z+x+1}\)
\(=\dfrac{xy+2x+1}{\left(y+1\right)\left(x+1\right)}+\dfrac{yz+2y+1}{\left(z+1\right)\left(y+1\right)}+\dfrac{z\left(x+2\right)+1}{\left(z+1\right)\left(x+1\right)}\)
\(=\dfrac{\left(xy+2x+1\right)\left(z+1\right)+\left(yz+2y+1\right)\left(x+1\right)+\left(xz+2z+1\right)\left(y+1\right)}{\left(x+1\right)\left(y+1\right)\left(z+1\right)}\)
\(=\dfrac{xyz+xy+2xz+2x+z+1+xyz+yz+2xy+2y+x+1+\left(xz+2z+1\right)\left(y+1\right)}{\left(x+1\right)\left(y+1\right)\left(z+1\right)}\)
\(=\dfrac{2xyz+3xy+2xz+3x+z+2+yz+2y+x+xyz+xz+2zy+2z+y+1}{\left(x+1\right)\left(y+1\right)\left(z+1\right)}\)
\(=\dfrac{3xyz+3xy+3xz+3yz+3x+3z+3y+3}{\left(x+1\right)\left(y+1\right)\left(z+1\right)}\)
\(=\dfrac{3\left(xyz+xy+xz+yz+x+z+y+1\right)}{\left(xy+x+y+1\right)\left(z+1\right)}\)
=3
Câu 14:
1:
f(0)=0+5=5
2:
Vì hệ số góc của y=ax+b là -1 nên a=-1
=>y=-x+b
Thay x=1 và y=2 vào y=-x+b, ta được:
b-1=2
=>b=3
