Question

已知x,y为实数，且满足

，求：的值

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Answer 1

解：y=√(x -1/2 )+√(1/2 -x ) +1/2
因为被开方数要大于等于0
所以 x-1/2≥0 且 1/2 -x≥0
x≥1/2 且 x≤1/2
所以 x=1/2
y=0+0+1/2=1/2

5x+|2y-1|-√(y²-2x+1)
=5×1/2+|2×1/2-1|-√[(1/2)²-2×1/2+1]
=5/2+0-√(1/4-1+1)
=5/2-√(1/4)
=5/2-1/2
=2

Answer 2

解：y=√(x -1/2 )+√(1/2 -x ) +1/2
因为被开方数要大于等于0
所以 x-1/2≥0 且 1/2 -x≥0
x≥1/2 且 x≤1/2
所以 x=1/2
y=0+0+1/2=1/2

5x+|2y-1|-√(y²-2x+1)
=5×1/2+|2×1/2-1|-√[(1/2)²-2×1/2+1]
=5/2+0-√(1/4-1+1)
=5/2-√(1/4)
=5/2-1/2
=2

Answer 3

解：y=√(x -1/2 )+√(1/2 -x ) +1/2
因为被开方数要大于等于0
所以 x-1/2≥0 且 1/2 -x≥0
x≥1/2 且 x≤1/2
所以 x=1/2
y=0+0+1/2=1/2
5x+|2y-1|-√(y²-2x+1)
=5×1/2+|2×1/2-1|-√[(1/2)²-2×1/2+1]
=5/2+0-√(1/4-1+1)
=5/2-√(1/4)
=5/2-1/2
=2