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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

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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