# A B D PLZZZZZ

as you are asking for multiple question.

so i suggest you to ask these questions seprately.

here i am answering its A part only.

let $y=\frac{{x}^{2}+2x+4}{x+2}$

$\Rightarrow y(x+2)={x}^{2}+2x+4$

$\Rightarrow yx+2y={x}^{2}+2x+4$

${x}^{2}+x(2-y)+(4-2y)=0$

since x is real so its Discriminent must be non-negative.

i.e ${B}^{2}-4AC\ge 0$

or $(2-y{)}^{2}-4(4-2y)\ge 0$

or ${y}^{2}+4y-12\ge 0$

or ${y}^{2}+6y-2y-12\ge 0$

or $(y+6)(y-2)\ge 0$

$\Rightarrow y\le -6ory\ge 2$

$\Rightarrow $minimum value of y will be 2

enjoy

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