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Prove that for all real values of x and ...

Prove that for all real values of `x and y ,x^2+2x y+3y^2-6x-2ygeq-11.`

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The correct Answer is:
` a lt 2`
Let ` x^(2) + 2xy + 3y^(2) - 6x - 2y + 11 ge 0 , AA x, y in `R
or ` x^(2) + (2y - 6) x + 3y^(2) - 2y + 11 ge 0 , AA x in `R
`rArr (2y - 6)^(2) - 4 (3y^(2) - 2y + 11) le 0, AA y in ` R
or `(y - 3)^(2) - (3y^(2) - 2y + 11) le 0, AA y in ` R
or ` 2y^(2) + 4y + 2 ge 0, AA y in `R
`rArr (y + 1)^(2) ge 0, AA y in R` , which is always true .
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