could I please have some help solving this equation for $x$ ?
${\sqrt{7x-5}} - {\sqrt{2x}} = {\sqrt{15 - 7x}}$
Thank you
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Hello and welcome to MSE. Consider adding some context to your problems to improve your chances of a good response. – Adam Hughes Mar 16 '15 at 10:00
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ok, then I get, – PlsHelpMe Mar 16 '15 at 10:01
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The range of possible values of $x$ is very limited. Identify it first and you will find a nice simple solution for the equation (inspection could help). – Claude Leibovici Mar 16 '15 at 10:01
1 Answers
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$${\sqrt{7x-5}} - {\sqrt{2x}} = {\sqrt{15 - 7x}}$$ $$7x-5 - 2{\sqrt{2x(7x-5)}}+2x =15 - 7x$$ $$16x-20 =2{\sqrt{2x(7x-5)}}$$ $$8x-10 ={\sqrt{2x(7x-5)}}$$ $$64x^2-160x+100=14x^2-10x$$ $$50x^2-150x+100=0$$ $$x^2-3x+2=0$$ $$x=1,x=2$$ only $x=2$ is solution
Adi Dani
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ohhhhh, ok, thank you very much, I was expanding the root in line 3 not dividing it by 2, thank you! – PlsHelpMe Mar 16 '15 at 10:08
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1+1 however a discussion on the correctness of the solutions found is probably called for.. I mean if the last equation has a negative solution is clear that it is not a solution to our original problem ;-) – Ant Mar 16 '15 at 10:10
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1@PlsHelpMe It is customary to accept answers that are most helpful to you. Do you have any reason not to accept this answer? – 5xum Mar 16 '15 at 11:19