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: $$- \frac{5}{7}$$
If $\sqrt{2x-5} + \sqrt{2x} = 7$, find $\sqrt{2x-5} - \sqrt{2x}$
0
$\begingroup$
roots
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0If you call $y = \sqrt{2 x - 5} - \sqrt{2 x}$, you obtain a system of two equations and two variables, easy to solve. – 2017-02-13
3 Answers
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By multiplying each other we get $$\sqrt { 2x-5 } +\sqrt { 2x } =7\\ \sqrt { 2x-5 } -\sqrt { 2x } =t\\ \\ 2x-5-2x=7t\\ t=-\frac { 5 }{ 7 } $$
2
Multiply the sum of roots and the difference of roots and simplify.
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0Uhhh. Difference of two squares. How did I miss that? – 2017-02-13
1
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.