If $\sqrt{2x-5} + \sqrt{2x} = 7$, find $\sqrt{2x-5} - \sqrt{2x}$

Question

I tried a few things but could not provide myself with a satisfying answer. Pointing me towards the solution rather than giving the answer or solution right up is as welcome.

Answer should be: $$- \frac{5}{7}$$

Answer 1

By multiplying each other we get $$\sqrt { 2x-5 } +\sqrt { 2x } =7\\ \sqrt { 2x-5 } -\sqrt { 2x } =t\\ \\ 2x-5-2x=7t\\ t=-\frac { 5 }{ 7 } $$

Answer 2

Multiply the sum of roots and the difference of roots and simplify.

Answer 3

Hint square both sides,

$(2x - 5) + 2x + 2\sqrt{2x(2x-5)} = 49$

$ 2\sqrt{2x(2x-5)} = 54 - 4x$

Square again and find x.

Then put into expression to get final answer.