Question

Observe o exemplo
(X+3)² - 24 = (x-3)²
X² + 6x + 9 -24 = x² - 6x+9
6x+6x=9+15
12x=24
X=2
Agora resolva as equações
A) (x+1)² -x² =17
B) x (x+5)=(x+1)² + 26
C) (x-4)² =x²- 40
D) 4 (x+2)² = (2x-3)²
ME AJUDE POR FAVOR!!!!

Answer 1

a) (x+1)²-x²=17
(x+1)*(x+1)-x²=17.
x²+x+x+1-x²=17.
x²+x+x-x²=17-1
2x=16
x=16/2
x=8

b)x*(x+5)=(x+1)²+26
x²+5x=(x+1)*(x+1)+26
x²+5x= x²+x+x+1+26
x²-x²+5x-x-x=26+1
3x=27
x=27/3
x=9

c) (x-4)²=x²-40
(x-4)*(x-4)=x²-40
x²-4x-4x+16=x²-49
x²-x²-4x-4x=-49+16
-8x=-33(-1)
a não pode ser negativo multiplica por: -1

8x=33
x=33/8
x=4,12

d)4*(x+2)²=(2x-3)²
(4x+8)²=(2x-3)*(2x-3)

(4x+8)*(4x+8)=4x²-6x-6x+9
16x²+32x+32x+64=4x²-6x-6x+9
16x²-4x²+32x+32x+6x+6x=9-64
12x²+76x=-55
12x²+76x+55=0
a=12 b=76 c=55
x=-b²±√b²-4*a*c/2a

x= -76±√76²-4*12*55/2*12
x=-76±√5.776-2.640/12
x=-76±√3.136/12
x=-76±56/12
x1= -76-56/12
x1=-132/12
x1=-11

x2=-76+56/12
x2=-20/12
x2=-1,66