Question

.El intervalo solución de la desigualdad x^2- 7x+ 10 ≤ 0 es : *

Answer 1

Factoriza {x}^{2}-7x+10x

2

−7x+10.

(x-5)(x-2)\le 0(x−5)(x−2)≤0

2 Despeja en función de xx.

x=5,2x=5,2

3 A partir de los valores de xx, tenemos estos 3 intervalos para probar.

\begin{aligned}&x\le 2\\&2\le x\le 5\\&x\ge 5\end{aligned}

x≤2

2≤x≤5

x≥5

4 Elige un punto de prueba para cada intervalo.

For the interval x\le 2x≤2:

Let's pick x=0x=0. Then, {0}^{2}-7\times 0+10\le 00

2

−7×0+10≤0.

After simplifying, we get 10\le 010≤0, which is false.

Descarta este intervalo..

For the interval 2\le x\le 52≤x≤5:

Let's pick x=3x=3. Then, {3}^{2}-7\times 3+10\le 03

2

−7×3+10≤0.

After simplifying, we get -2\le 0−2≤0, which is true.

Mantén este intervalo..

For the interval x\ge 5x≥5:

Let's pick x=6x=6. Then, {6}^{2}-7\times 6+10\le 06

2

−7×6+10≤0.

After simplifying, we get 4\le 04≤0, which is false.

Descarta este intervalo..

5 Por lo tanto,

2\le x\le 52≤x≤5