Question

Answer 1

a: \(\left(x+1\right)^2+\left(3-x\right)\left(x+3\right)>=8\)

=>\(x^2+2x+1+9-x^2>=8\)

=>2x+10>=8

=>2x>=-2

=>x>=-1

b: \(\left(x+2\right)^2-\left(x-2\right)^2< =2\left(x+1\right)\)

=>\(x^2+4x+4-x^2+4x-4< =2x+2\)

=>8x<=2x+2

=>6x<=2

=>\(x< =\dfrac{1}{3}\)

c: \(2\left(x+3\right)\left(x+4\right)>\left(x-2\right)^2+\left(x-1\right)^2+5\)

=>\(2\left(x^2+7x+12\right)>x^2-4x+4+x^2-2x+1+5\)

=>\(2x^2+14x+24>2x^2-6x+11\)

=>14x+24>-6x+11

=>20x>-13

=>\(x>-\dfrac{13}{20}\)

d: \(5x^2-18x+20-\left(2x-3\right)^2>0\)

=>\(5x^2-18x+20-4x^2+12x-9>0\)

=>\(x^2-6x+11>0\)

=>\(\left(x-3\right)^2+2>0\)(luôn đúng)