Question

How do I find the extraneous solution of y−5=4√y?

Answer 1

The answer is

y

=

1

First, let's square both members:

y

−

5

=

4

√

y

⇒

(

y

−

5

)

2

=

16

y

⇒

y

2

−

26

y

+

25

=

0

Then let's solve the equation:

y

1

,

y

2

=

13

±

√

169

−

25

=

13

±

12

⇒

y

1

=

1

,

y

2

=

25

We know there are no other roots because of the fundamental theorem of algebra.

y

2

is an acceptable answer because

25

−

5

=

4

⋅

√

25

does make sense, but

y

1

is not acceptable because

−

4

=

4

√

1

does not make any sense because we chose to consider the positive branch of the square root function.

So the extraneous solution is

y

2

. hope you like it