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If the line y=x touches the curve y=x^2+...

If the line `y=x` touches the curve `y=x^2+b x+c` at a point `(1,\ 1)` then `b=1,\ c=2` (b) `b=-1,\ c=1` (c) `b=2,\ c=1` (d) `b=-2,\ c=1`

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Given that y=x touches (1) when,
`x=x^2+bx+c ........(2)`
for x and y at (1,1)
`1=1+b+c`
`b+c=0`
`b=−c`
...
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