Bài 2.5:
a: \(\left(x+1\right)\left(x+3\right)-x\left(x+2\right)=7\)
=>\(x^2+4x+3-x^2-2x=7\)
=>2x+3=7
=>2x=4
=>x=4/2=2
b: \(2x\left(3x+5\right)-x\left(6x-1\right)=33\)
=>\(6x^2+10x-6x^2+x=33\)
=>11x=33
=>x=33/11=3
c: \(\left(3x^2-x+1\right)\left(x-1\right)+x^2\left(4-3x\right)=\dfrac{5}{2}\)
=>\(3x^3-3x^2-x^2+x+x-1+4x^2-3x^3=\dfrac{5}{2}\)
=>2x-1=5/2
=>2x=7/2
=>\(x=\dfrac{7}{2}:2=\dfrac{7}{4}\)
d: \(\left(12x-5\right)\left(4x-1\right)+\left(3x-7\right)\left(1-16x\right)=81\)
=>\(48x^2-12x-20x+5+3x-48x^2-7+112x=81\)
=>\(83x-2=81\)
=>83x=83
=>\(x=\dfrac{83}{83}=1\)
e: \(\left(x-3\right)\left(x^2+3x+9\right)+x\left(5-x^2\right)=6x\)
=>\(x^3-27+5x-x^3=6x\)
=>6x=5x-27
=>6x-5x=-27
=>x=-27
f: \(\left(x-2\right)^3-x\left(x+1\right)\left(x-1\right)+6x^2=5\)
=>\(x^3-6x^2+12x-8-x\left(x^2-1\right)+6x^2=5\)
=>\(x^3+12x-8-x^3+x=5\)
=>13x-8=5
=>13x=13
=>\(x=\dfrac{13}{13}=1\)
g: \(\left(x+3\right)^3-x\left(3x+1\right)^2+\left(2x+1\right)\left(4x^2-2x+1\right)-3x^2=54\)
=>\(x^3+9x^2+27x+27-x\left(9x^2+6x+1\right)+8x^3+1-3x^2=54\)
=>\(9x^3+6x^2+27x+28-9x^3-6x^2-x=54\)
=>\(26x+28=54\)
=>26x=54-28=26
=>\(x=\dfrac{26}{26}=1\)
h: \(\left(x-2\right)^3-\left(x+5\right)\left(x^2-5x+25\right)+6x^2=11\)
=>\(x^3-6x^2+12x-8+6x^2-\left(x^3+125\right)=11\)
=>\(x^3+12x-8-x^3-125=11\)
=>12x-133=11
=>12x=11+133=144
=>x=144/12=12
