If $x$ and $y$ be real , and $9 x^{2} + 2 x y + y^{2} - 92 x - 20 y + 244 = 0$ then the value of $x$ can be

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Solution

The correct option is B 3
$9 x^{2} + 2 x y + y^{2} - 92 x - 20 y + 244 = 0$
Given y is real,
$y^{2} + (2 x - 20) y + 9 x^{2} - 92 x + 244 = 0$
${(2 x - 20)}^{2} - 4 (9 x^{2} - 92 x + 244) \geq 0$
${(x - 10)}^{2} - (9 x^{2} - 92 x + 244) \geq 0$
$- 8 x^{2} + 72 x - 144 \geq 0$
$x^{2} - 9 x + 18 \leq 0$
$∴ x ϵ [3, 6]$

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