How do you solve #\sqrt { x + 3} + \sqrt { x } = 3#?

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Answer 1 · 2016-11-30T09:27:43

1

To make the expression real, #x >=0#.

Squaring,

#x+3 + x +2sqrt(x(x+3))=9#. So,

#sqrt(x(x+3))=3-x#

Again squaring,

#x^2+3x=x^2-6x+9#. And so,

x = 1.

graph{sqrt(x+3)+sqrt(x)-3 [-10, 10, -5, 5]}