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  4. For x ≥ 0, the smallest value of expression y=(3 x2+6 x+6/2(x+1)) is

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Q. For $x \geq 0$, the smallest value of expression $y=\frac{3 x^2+6 x+6}{2(x+1)}$ is

Complex Numbers and Quadratic Equations

Solution:

$y=\frac{3\left(x^2+2 x+1\right)+3}{2(x+1)}$
$y=\frac{3(x+1)^2}{2(x+1)}+\frac{3}{2(x+1)} $
$y=\frac{3}{2}(x+1)+\frac{3}{2(x+1)} $
$y_{\min } \geq 2 \sqrt{\frac{3}{2} \times \frac{3}{2}}$
$y_{\min } \geq 3 $