d: \(\left(1-x\right)^3+x\left(x+2\right)^2-\left(x+5\right)=0\)
=>\(-x^3+3x^2-3x+1+x\left(x^2+4x+4\right)-x-5=0\)
=>\(-x^3+3x^2-4x-4+x^3+4x^2+4x=0\)
=>\(7x^2-4=0\)
=>\(x^2=\dfrac{4}{7}\)
=>\(x=\pm\dfrac{2}{\sqrt{7}}\)
e: \(\left(x-3\right)^3-\left(x-3\right)\left(x^2+3x+9\right)+9\left(x+1\right)^2=15\)
=>\(x^3-9x^2+27x-27-\left(x^3-27\right)+9\cdot\left(x^2+2x+1\right)=15\)
=>\(x^3-9x^2+27x-27-x^3+27+9x^2+18x+9=15\)
=>45x+9=15
=>45x=6
=>\(x=\dfrac{6}{45}=\dfrac{2}{15}\)
f: \(x\left(x-5\right)\left(x+5\right)-\left(x+2\right)\left(x^2-2x+4\right)=3\)
=>\(x\left(x^2-25\right)-x^3-8=3\)
=>\(x^3-25x-x^3-8=3\)
=>-25x-8=3
=>-25x=11
=>\(x=-\dfrac{11}{25}\)
`d)(1-x)^3+x(x+2)^2-(x+5)=0`
`<=>1-3x+3x^2-x^3+x^3+4x^2+4x-x-5=0`
`<=>7x^2-4=0`
`<=>x^2=4/7`
`<=>x=+-2/sqrt7`
`e)(x-3)^3-(x-3)(x^2+3x+9)+9(x+1)^2=15`
`<=>(x-3)(x^2-6x+9-x^2-3x-9)+9(x^2+2x+1)=15`
`<=>(x-3).(-9x)+9x^2+18x+9=15`
`<=>-9x^2+27x+9x^2+18x-6=0`
`<=>45x-6=0`
`<=>x=2/15`
`f)x(x-5)(x+5)-(x+2)(x^2-2x+4)=3`
`<=>x(x^2-25)-(x^3+8)=3`
`<=>x^3-25x-x^3-8-3=0`
`<=>-25x-11=0`
`<=>x=-11/25`
