Question

porfa ayuda es una tarea de la uni urgente si la hago paso el curso (solo tengo que resolver 8 de estas)

Answer 1

Respuesta:

1. $x^{2} \geq 1 ; x\leq \sqrt{1}; x\leq +/- 1$

2.

$x(8+5x)\geq 0; x\geq 0 , 5x\geq -8 \\x\geq -8/5$

3.

$x(x-3)-2x(x-2)+3x<0\\x^{2} -3x-2x^{2} +4x+3x<0\\-x^{2} +4x<0; x(-x+4)<0; x<0\\-x<-4; x<4$

4.$4x^{2} -1<0; x^{2} <1/4; x<\sqrt{1/4}$

5.

$3x^{2} -5x<0; x(3x-5<0); \\x<0\\ x<5/3$

6.

$x(x-5)-2x(x+3)+6\leq x^{2} -11x\\x^{2} -5x-2x^{2} -6+6\leq x^{2} -11x\\-x^{2} +6x; x(-x^{2} +6); x\leq 0\\-x^{2} +6\leq 0; -x^{2} \leq -6; x^{2} \leq 6$

7. $x^{2} -13x+40<0$

*formula de segundo grado* $13+/-\sqrt{(13^{2}-4(40) } /2$

(13+/-3) / 2 ; x<(13+3)/2 ; x<8.   x<(13-3)/2; x<5

8. $2x^{2} +3\leq 7x; 2x^{2} -7x+3\leq 0$

*formula de segundo grado* $7+/-\sqrt{49-4(2)(3)} \\7+/-\sqrt{49-24}$

$x\leq (7+5)/2 ; x\leq 6\\x\leq (7-5)/2 ; x\leq 1$