Question

Prove that x=√-5x-6 has no solution.

Answer 1

Answer:

See explanation below.

Step-by-step explanation:

We need to prove that there are no solutions of the equation: x = $\sqrt{-5x-6}$

Let's start trying to solve this equation: $x = \sqrt{-5x+6} \\x^{2} =-5x + 6\\x^{2} +5x - 6 = 0$

To solve this equation, by factorizing the equation we get:

$x^{2} +5x-6 = 0\\(x +6)(x-1) = 0\\x=-6\\x=1$

• Now we're going to substitute these numbers in the original equation:

For x = -6 we have:

x = $x=\sqrt{5x-6} \\6=\sqrt{5(-6)-6} \\6=\sqrt{-30-6} \\6= \sqrt{-36}$

But √-36 has no solution in the real numbers and therefore it cannot equal 6.

• Now the second, x = 1

$x = \sqrt{-5x-6} \\1=\sqrt{-5(1)-6}\\1=\sqrt{-5-6} \\1=\sqrt{-11} \\1\neq \sqrt{-11}$

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