sqrt(x+2sqrt(x-1))+sqrt(x-2sqrt(x-1))=1

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Solution for sqrt(x+2sqrt(x-1))+sqrt(x-2sqrt(x-1))=1 equation: 


Simplifying
sqrt(x + 2sqrt(x + -1)) + sqrt(x + -2sqrt(x + -1)) = 1

Reorder the terms:
qrst(x + 2qrst(-1 + x)) + sqrt(x + -2sqrt(x + -1)) = 1
qrst(x + (-1 * 2qrst + x * 2qrst)) + sqrt(x + -2sqrt(x + -1)) = 1
qrst(x + (-2qrst + 2qrstx)) + sqrt(x + -2sqrt(x + -1)) = 1

Reorder the terms:
qrst(-2qrst + 2qrstx + x) + sqrt(x + -2sqrt(x + -1)) = 1
(-2qrst * qrst + 2qrstx * qrst + x * qrst) + sqrt(x + -2sqrt(x + -1)) = 1

Reorder the terms:
(qrstx + -2q2r2s2t2 + 2q2r2s2t2x) + sqrt(x + -2sqrt(x + -1)) = 1
(qrstx + -2q2r2s2t2 + 2q2r2s2t2x) + sqrt(x + -2sqrt(x + -1)) = 1

Reorder the terms:
qrstx + -2q2r2s2t2 + 2q2r2s2t2x + qrst(x + -2qrst(-1 + x)) = 1
qrstx + -2q2r2s2t2 + 2q2r2s2t2x + qrst(x + (-1 * -2qrst + x * -2qrst)) = 1
qrstx + -2q2r2s2t2 + 2q2r2s2t2x + qrst(x + (2qrst + -2qrstx)) = 1

Reorder the terms:
qrstx + -2q2r2s2t2 + 2q2r2s2t2x + qrst(2qrst + -2qrstx + x) = 1
qrstx + -2q2r2s2t2 + 2q2r2s2t2x + (2qrst * qrst + -2qrstx * qrst + x * qrst) = 1

Reorder the terms:
qrstx + -2q2r2s2t2 + 2q2r2s2t2x + (qrstx + 2q2r2s2t2 + -2q2r2s2t2x) = 1
qrstx + -2q2r2s2t2 + 2q2r2s2t2x + (qrstx + 2q2r2s2t2 + -2q2r2s2t2x) = 1

Reorder the terms:
qrstx + qrstx + -2q2r2s2t2 + 2q2r2s2t2 + 2q2r2s2t2x + -2q2r2s2t2x = 1

Combine like terms: qrstx + qrstx = 2qrstx
2qrstx + -2q2r2s2t2 + 2q2r2s2t2 + 2q2r2s2t2x + -2q2r2s2t2x = 1

Combine like terms: -2q2r2s2t2 + 2q2r2s2t2 = 0
2qrstx + 0 + 2q2r2s2t2x + -2q2r2s2t2x = 1
2qrstx + 2q2r2s2t2x + -2q2r2s2t2x = 1

Combine like terms: 2q2r2s2t2x + -2q2r2s2t2x = 0
2qrstx + 0 = 1
2qrstx = 1

Solving
2qrstx = 1

Solving for variable 'q'.

Move all terms containing q to the left, all other terms to the right.

Divide each side by '2rstx'.
q = 0.5r-1s-1t-1x-1

Simplifying
q = 0.5r-1s-1t-1x-1

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