Question

the number integral solution of x+2 / x2 +1 > 1/2

Answer 1

Answer:

If the given inequality is : -

$\frac{x + 2}{ {x}^{2} + 1} \geqslant \frac{1}{2}$

$\frac{x + 2}{ {x}^{2} + 1} - \frac{1}{2} \geqslant 0$

$\frac{2(x + 2) - {x}^{2} + 1}{2( {x}^{2} + 1) } \geqslant 0$

$\frac{2x + 4 - {x}^{2} - 1}{2( {x}^{2} + 1) } \geqslant 0$

$\frac{ - {x}^{2} + 2x + 3}{ {2x}^{2} + 1 } \geqslant 0$

${ - x}^{2} + 2x + 3 \geqslant 0$

${x}^{2} + 3x - x - 3 \leqslant 0$

$(x + 3)(x - 1) \leqslant 0$

$Therefore, \: \: x = - 3 \: , \: 1$

Integral solutions are -3, -2, -1, 0, 1

The number of integral solutions are 5.

I Hope It Will Help!

^_^

${x}^{2} - 2x - 3 \leqslant 0$