How do you solve #\sqrt { 3x + 9} - 2\sqrt { x } = 0#?

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Answer 1 · 2017-07-14T22:45:04

#x = 9#

We jave: #sqrt(3 x + 9) - 2 sqrt(x) = 0#

Adding #2 sqrt(x)# to both sides of the equation:

#Rightarrow sqrt(3 x + 9) - 2 sqrt(x) + 2 sqrt(x) = 0 + 2 sqrt(x)#

#Rightarrow sqrt(3 x + 9) = 2 sqrt(x)#

Squaring both sides:

#Rightarrow (sqrt(3 x + 9))^(2) = (2 sqrt(x))^(2)#

#Rightarrow 3 x + 9 = 4 x#

Collecting like terms:

#Rightarrow 4 x - 3 x = 9#

#therefore x = 9#