Question

Solve the equation, and check the solutions 3√(x+2) + √(x-4)=0.

Answer 1

No solution

Explanation:

Given that,

`3√(x+2)+√(x-4)=0`

Box x under square root. Inside the square root number must be positive.

Therefore,

`x+2\geq 0`

`x\geq -2`

`x-4\geq0`

`x\geq4`

`3√(x+2)+√(x-4)=0`

`3√(x+2)=-√(x-4)`

Taking square both sides

`(3√(x+2))^2=(-√(x-4))^2`

`9(x+2)=(x-4)`

`9x+18=x-4`

`9x-x=-4-18`

`8x=-22`

`x=-(11)/(4)`

Now take intersection of all three solution.

`x=-(11)/(4)`,
`x\geq4`,
`x\geq -2`

No intersection value of x

No solution