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You were kind of lucky (because of the construction of the question), that the sum (a-1)² + (b-1)² + (c-1)² + (d-1)² was zero (0) and not some positive number! That's the only occasion, that you can follow, that all these squares are zero. For negative, there are no real solutions, for positive, you don't know how to continue. For zero, you get what you want. So what about sqrt(x-1)+sqrt(2x-3)+sqrt(3x-5)+sqrt(4x-7) = 5x - 6.005 ? Are you helpless now? The sum of squares is now 0.01 ! You'll get infinite many solutions now, e.g. a=1.1 or a=0.9 with b=c=d=1 or b=1.1 or b=0.9 with a=c=d=1 or ... and everything in between!
I think you do a terrific job explaining all the steps. Your methods may be a bit long, but they are very helpful to struggling math students. I taught high school math for 25 years and I always learn something from his videos. Please keep them coming. Dr. Kapadia 🌺
