Verified answer

√(8 - 2x) = x

8 - 2x = x²

x² + 2x - 8 = 0

= (x + 4)(x - 2)

Answer: a. {2}, x = - 4 or x = 2

Um.... none.

√8 - 2x = x

First isolate x terms by adding 2x to both sides.

√8 = 3x

√8 = 2√2 (as √8 = √(4*2) or √4 * √2

Divide both sides by 3.

(2√2)/3 = x

If d. Ø means no solutions available, then d is the right answer.

It should be written √(8-2x) = x.

Square both sides of the equation

8 - 2x = x²

x² + 2x - 8 = 0

(x-2)(x+4) = x² + 2x - 8

x = 2, -4

Square both sides:

(√8-2x)^2 = x^2

8 - 2x = x^2

Then bring everything to one side to make a quadratic equation:

x^2 + 2x - 8 = 0

And factor:

x^2 + 2x - 8 = (x + 4)(x - 2)

So your solution set is {x | x = 2, -4}

√8 - 2x = x

3x = √8

x = √8 / 3

x = 2√2 / 3

√(8-2x) = x

square both sides

8-2x=x²

0=x²+2x-8

0=(x+4)(x-2)

x = -4 or 2

c {2,-4}

√(8 - 2x) = x

8 - 2x = x^2

x^2 + 2x - 8 = 0

x^2 + 4x - 2x - 8 = 0

(x^2 + 4x) - (2x + 8) = 0

x(x + 4) - 2(x + 4) = 0

(x + 4)(x - 2) = 0

x + 4 = 0

x = -4

x - 2 = 0

x = 2

∴ x = -4, 2

(answer c)

sqrt ( 8 - 2x ) = x .......(1)

Squaring both sides

8 - 2x = x^2

x^2 + 2x - 8 = 0

( x + 4 )( x - 2 ) = 0

x = - 4 or x = 2.

.................................................................................

But putting x = - 4 in (1) gives sqrt ( 16 ) = -4 which is false.

Such a root is called an extraneous root.

.................................................................................

Putting x = 2 gives sqrt ( 4 ) = 2 which is ' legal '.

..................................................................................

Hence, there is only one correct solution, namely, a.{ 2 }........Ans.