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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: $$- \frac{5}{7}$$

SarpSTA
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  • If you call $y = \sqrt{2 x - 5} - \sqrt{2 x}$, you obtain a system of two equations and two variables, easy to solve. – joseabp91 Feb 13 '17 at 18:52

3 Answers3

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

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

Hagen von Eitzen
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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.

Amar
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