Question

Resolver las siguientes desigualdades cuadráticas.

a) 2 − 7 + 12 < 0

b) 2 − 3 + 2 ⩾ 0

c) 42 − 10 + 6 ⩾ 0

d) 22 + 7 ⩽ 3

e) 121 − 22 + 2 > 0​

Answer 1

Respuesta:

a)  

 $x^{2} -7x +12 <0\\\\x^{2} -7x +12 = 0\\(x-4)(x-3)\\\\x= 4\\x= 3$

b)

$x^{2} -3x+2\geq 0\\\\x^{2} -3x +2 = 0\\(x-2)(x-1)\\\\x= 2\\x= 1$

c)

$4x^{2} -10x +6 \geq 0\\\\4x^{2} -10x+6 = 0\\\\\frac{(4x-6)(4x-4)}{4}\\\\\frac{2(2x-3)2(2x-2)}{4}\\\\(2x-3)(2x-2)\\\\2x-3 = 0\\2x = 3\\x = 3/2\\x =1.5\\\\2x-2 =0\\2x = 2\\x = 2/2\\x = 1$

d)

$2x^{2} +7x\leq 3\\\\-2x^{2} -7x+3 =0\\\\\frac{(-2x-6)(-2x-1)}{-2}\\\\\frac{-2(x+3)(-2x-1)}{-2}\\\\(x+3)(-2x-1)\\\\x= -3\\\\-2x-1 = 0\\\\-2x = 1\\x= 1/-2 \\x = -0.5$

e)

$121 -22x +x^{2} > 0\\\\x^{2} -22x+121 = 0\\\\(x-11)(x-11)\\\\x= 11\\\\x= 11$

Explicación paso a paso: