SOLUTION: the square root of x minus 3 square root of x with an index of 4 minus 4 equals 0

Question 201492This question is from textbook precalculus
: the square root of x minus 3 square root of x with an index of 4 minus 4 equals 0 This question is from textbook precalculus

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The easiest way to do this is based on understanding that . This is not hard to see if you understand fractional exponents: and . So . Using the appropriate rule for exposnents (

If we let then . Substituting these into
we get

This equation can be easily solved by factoring:

Since a product of zero means one of the factors must be zero:
y-4=0 or y+1=0
Adding 4 to both sides of the first equation and subtracting 1 from both sides of the second we get:
y=4 or y=-1
Now we substitute back in for y:
or
We reject the second equation because by definition must not be negative. To solve the first equation we raise both sides to the 4th power:
which gives:
x = 256
Checking:

16 - 3*4 - 4 = 0
16 - 12 - 4 = 0
0 = 0 Check!!
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