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If x and y are two real quantities conne...

If x and y are two real quantities connected by the equation `9x^2+2xy+y^2-92x-20y+244=0` then will x lie between 3 and 6 and y between 1 and 10.

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`9x^2+2xy+y^2-92x-20y+244=0`
`9x^2+x(2y-92)+y^2-20y+244=0`
`x=(-(2y-92)pmsqrt((2y-92)^2-4*9(y^2-20y+244)))/(2*9)`
`D>0`
`(2y-92)^2-4*9(y^2-20y+244)>0`
`(y-46)^2-9(y^2-20y+244)>0`
`y^2+2116-9y^2+180y-2196>0`
`8y^2-180y+80<0`
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