How do you solve #sqrt(x-6)=sqrt(1/3x)=0#?

Question

Avery Alexander · Accepted Answer

No value of #x# satisfies both equalities.

#sqrt(x-6)=sqrt(1/3x)# #color(white)("XXX")rarrx-6=1/3x# #color(white)("XXX")rarr3x-18=x# #color(white)("XXX")rarr2x=18# #color(white)("XXX")rarrx=9# ด ฟฟ ฟ ฟฟ #sqrt(1/3x)=0# #color(white)("XXX")rarrx=0# ด ฟฟ ฟ ฟฟ #sqrt(x-6)=0# #color(white)("XXX")rarrx-6=0# #color(white)("XXX")rarrx=6#

Jameson Allen · Answer

undefined To solve the equation sqrt(x-6) = sqrt(1/3x) = 0, we can follow these steps:

1. Start by isolating one of the square roots. Let's isolate sqrt(x-6) first.
   sqrt(x-6) = 0

2. Square both sides of the equation to eliminate the square root.
   (sqrt(x-6))^2 = 0^2
   x - 6 = 0

3. Solve for x by adding 6 to both sides of the equation.
   x = 6

4. Now, let's isolate the other square root, sqrt(1/3x).
   sqrt(1/3x) = 0

5. Square both sides of the equation.
   (sqrt(1/3x))^2 = 0^2
   1/3x = 0

6. Solve for x by multiplying both sides of the equation by 3.
   3 * (1/3x) = 0 * 3
   1/x = 0

7. Since 1/x cannot equal zero, there is no solution for this equation.

Therefore, the only solution to the original equation sqrt(x-6) = sqrt(1/3x) = 0 is x = 6.