How do you solve #\sqrt { x } - 4= \sqrt { 9x }#?
2 Answers
See a solution process below:
Explanation:
FIrst, add
Next, square both sides of the equation to eliminate the radicals while keeping the equation balanced:
(Note: use this rule to multiply the left side of the equation:)
Solution for
Then, we can combine like terms:
Now, divide each side of the equation by
Solution for
Then, we can combine like terms:
Now, divide each side of the equation by
The Solutions Are:
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(Note, if you substitute these into the original equation the are two things to notice:
- The square root of a number produces both a positive and negative result.
- When dealing with square roots there can be extraneous solutions.
No solution.
Explanation:
#sqrtx-4=sqrt(9x)#
Isolate the radicals by subtracting
#-4=sqrt(9x)-sqrtx#
Split
#-4=(sqrt9*sqrtx)-sqrtx#
#-4=3sqrtx-sqrtx#
Subtract the radicals.
#-4=2sqrtx#
Divide both sides by
#-2=sqrtx#
#sqrtx=-2#
Now, we are left with