Find`sqrt(x^2 +2x+(y-1)^2 -2xy)` ` `
Please state your workings clearly.
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First evaluate the expression under the square root sign:
`x^2 + 2x + (y-1)^2 - 2xy = x^2 + 2x + y^2 - 2y + 1 - 2xy`
`= x^2 + y^2 -2xy + 2(x-y) + 1`
`(x-y)^2 = x^2 + y^2 - 2xy`
`[(x-y)+1][(x-y)+1] = (x-y)^2 + 2(x-y) + 1`
`= (x^2 + y^2 - 2xy) + 2(x-y) + 1`
which is the expression we require.
Hence the expression under the square root sign simplifies to
`[(x-y)+1][(x-y)+1] = [(x-y)+1]^2`
Thus, square rooting this the result is
`(x-y) + 1`
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