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# Solve This!

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Senior Manager
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Solve This! [#permalink]  26 Jan 2004, 16:44
Solve sqrt(5x^2 - 6x + 8) - sqrt(5x^2 - 6x - 7) = 1
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Pls include reasoning along with all answer posts.
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Este examen me conduce jodiendo loco

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Pretty long calculation, uffffffffffff taking - sqrt 5x^2-6x-7 to the otherside and squaring both sides and then after cancelling some terms we get 7=sqrt 5x^2-6x-7 again squaring both sides we get 5x^2-6x-56=0 solve for x we get 4 and -14/5
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It is not clear rakesh..would u mind to show me stepwise..if its not bothering u much.. coz i am getting soemting diff..
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shubhangi

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sqrt (5x^2-6x+8) - sqrt (5x^2-6x-7) =1 is the question
taking the term - sqrt(5x^2-6x-7) to other side we get
sqrt (5x^2-6x+8) = 1 + sqrt (5x^2-6x-7)
Now squaring on both sides we get

5x^2-6x+8 = 1 + 5x^2 -6x-7 + 2sqrt(5x^2-6x-7)
we can cancel out 5x^2 and -6x, then we get 14= 2sqrt(5x^2-6x-7)
which means , 7 = sqrt(5x^2-6x-7) , now squaring again we get 49= 5x^2-6x-7, ie 5x^2-6x-56=0 now solve for x
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Let 5x^-6x+8 = A
Therefore sqrtA-sqrt (A+5)=1
squaring both sides:
A+A-15-2*sqrt(A^2-15*A)=1
transferring:
2A-16=2*sqrt(A^2-15*A)
factoring by 2:
A-8=sqrt(A^2-15*A)
squaring again:
=>A^2-16*A+64=A^2-15*A
=>A=64
=>5X^2-6X+8 = 64
=>5X^2-6X-56=0
=>(5X+14)(X-4)=0
=>X= 4, -14/5
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