Solve the following equation: x + √(x+3) = 3 + 3√(1-x)

Question

Solve the following equation:

`x + √(x+3) = 3 + 3√(1-x)`

Answer 1

`x+√(x+3)=3+3√(1-x)`

`Remove~ Square ~root`

`-36x^3+252x^2-540x+324=`

`x^4-32x^3+286x^2-480x+225`

`Now ~\mathrm{Switch\:sides}`

`x^2-6x√(-x+1)-15x+18√(-x+1)+18=x+3`

`\mathrm{Subtract\:}x^2-15x\mathrm{\:from\:both\:sides}`

`x^2-6x√(-x+1)-15x+18√(-x+1)+18-\left(x^2-15x\right)=`

`x+3-\left(x^2-15x\right)`

`New ~Simplify`

`-6x√(-x+1)+18√(-x+1)+18=-x^2+16x+3`

`Subtract ~18~ from ~ both~ sides`

`-6x√(-x+1)+18√(-x+1)+18-18=-x^2+16x+3-18`

`Simplify`

`-6x√(-x+1)+18√(-x+1)=-x^2+16x-15`

`Now~ factor:`

`-6x√(-x+1)+18√(-x+1)(-x+3)`

`6√(-x+1)\left(-x+3\right)=-x^2+16x-15`

`Solve~~-36x^(3)+252x^(2) -540x+324=x^(4) -32x^(3) +286x^(2) -480x+225=`

`x=1,\:x=-3`

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