Question

Solve the radical expression. Check your solution.
\[ \sqrt{2-x} =x\]

Answer 1

The given radical expression is
`√(2-x)=x`

Squaring on both the sides of the equation, we get

`2-x=x^(2)`

Bringing all the variables and constant to the right side of the expression, so we get:

`x^(2)+x-2=0`

By comparing the above expression with the standard form
`ax^(2)+bx+c=0`

we get a=1, b=1 and c= -2

Discrimant(D) =
`b^(2)-4ac`

Discrimant(D)=
`(1)^(2)-4(1)(-2)`

D=9

`x=(-b+√(D))/(2a) and x=(-b-√(D))/(2a)`

`x=(-1+√(9))/(2) and x=(-1-√(9))/(2)`

`x=(-1+3)/(2) and x=(-1-3)/(2)`

x= -1 and 2 are the required solutions of the given radical expression.