Answer:
See explanation below.
Step-by-step explanation:
We need to prove that there are no solutions of the equation: x = [tex]\sqrt{-5x-6}[/tex]
Let's start trying to solve this equation: [tex]x = \sqrt{-5x+6} \\x^{2} =-5x + 6\\x^{2} +5x - 6 = 0[/tex]
To solve this equation, by factorizing the equation we get:
[tex]x^{2} +5x-6 = 0\\(x +6)(x-1) = 0\\x=-6\\x=1[/tex]
For x = -6 we have:
x = [tex]x=\sqrt{5x-6} \\6=\sqrt{5(-6)-6} \\6=\sqrt{-30-6} \\6= \sqrt{-36}[/tex]
But √-36 has no solution in the real numbers and therefore it cannot equal 6.
[tex]x = \sqrt{-5x-6} \\1=\sqrt{-5(1)-6}\\1=\sqrt{-5-6} \\1=\sqrt{-11} \\1\neq \sqrt{-11}[/tex]
Since the left side is different than the right one, this is not a solution.
Therefore the equation has no solution in the real numbers
