Question

1)Efectuati calculele
a) (x+1)^2-x(x+5)
b) (x-3)(x+3)-(x-2)^2
c) x(x+4)-(x+2)^2
d) (2x+1)^2-(x+1)^2

Answer 1

[tex]a) (x+1)^2-x(x+5)= x^{2} +2x+1- x^{2} -5x=1-3x\\ b) (x-3)(x+3)-(x-2)^2= x^{2} -3^2-( x^{2} -4x+4)= x^{2} -9- x^{2} +\\+4x-4=4x-13\\ c) x(x+4)-(x+2)^2= x^{2} +4x- (x^{2} +4x+4)=x^{2} +4x-x^{2}-4x\\-4=-4\\ d) (2x+1)^2-(x+1)^2=(2x)^2+4x+1-( x^{2} +2x+1)=4 x^{2} +4x+1\\- x^{2} -2x-1=3 x^{2} +2x=x(3x+2)\\[/tex]

Answer 2

a) (x+1)^2-x(x+5) =0⇒x^2+2x+1-x^2-5x =0⇒ -3x+1=0 ⇒-3x =-1⇒x = 1/3
b) (x-3)(x+3)-(x-2)^2 =x^2-3^2-x^2+4x-2^2= x^2-9-x^2+4x-4 =0⇒ 4x-13 = 0 ⇒4x=13⇒x= 13/4
c) x(x+4)-(x+2)^2=0 ⇒x^2+4x-x^2-4x-4 =-4
d) (2x+1)^2-(x+1)^2 =0⇒4x^2+4x+1-x^2-2x-1 = 0⇒3x^2+2x = 0 ⇒x(3x+2) = 0$\left \{ {{x=0} \atop {3x+2=0}} \right.$ ⇒$\left \{ {{x=0} \atop {3x=-2}} \right.$⇒$\left \{ {{x=0} \atop {x=- \frac{2}{3} }} \right.$