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(x+2)^6 = 4^6We put x+2 = 4 ythen y^6 = 1y^3 = 1 ,-1y = 1 , -1, w , w^2 , - w , - w^2x= 4 y - 2 hence x = 2 , -6 , 4 w-2 , 4 w^2 -2 , -4 w-2 , - 4 w^2 -2x= 2 , - 6 , - 4+2√3 i , - 4-2√3 i , - 2 i√3 , 2 i√3
let (x+2)=A : A^6=2^12 ; A=(2^12)^1/6 ; A=2^2 or A=4, as A=x+2 or 4=X+2, so X=2
x_j = 4[cos(jπ/3) + i*sin(jπ/3)]-2, j=0, 1, ..., 5
Sorry sir, but I have a querie Can't it be like that:(x+2)⁶ = 2¹²=x+2 = 6rooted 2¹²=x+2 = 2^12/6=x+2 = 2²=x+2 = 4 =x =4-2=x =2??
Can't it be like that:(x+2)⁶=2^12=x+2 = 6 rooted (2)¹²=x+2 = (2)^12/6=x+2 = (2)²=x+2 = 4=x = 4 -2=x = 2
Sorry sir, but I have a querie Can't it be like that:(x+2)⁶ = 2¹²=x+2 = 6rooted 2¹²=x+2 = 2^12/6=x+2 = 2²=x+2 = 4 =x =4-2=x =2??😅
You've found one solution. You need to find six roots!
(x+2)^6 = 4^6
We put x+2 = 4 y
then y^6 = 1
y^3 = 1 ,-1
y = 1 , -1, w , w^2 , - w , - w^2
x= 4 y - 2 hence
x = 2 , -6 , 4 w-2 , 4 w^2 -2 , -4 w-2 , - 4 w^2 -2
x= 2 , - 6 , - 4+2√3 i , - 4-2√3 i , - 2 i√3 , 2 i√3
let (x+2)=A : A^6=2^12 ; A=(2^12)^1/6 ; A=2^2 or A=4, as A=x+2 or 4=X+2, so X=2
x_j = 4[cos(jπ/3) + i*sin(jπ/3)]-2, j=0, 1, ..., 5
Sorry sir, but I have a querie
Can't it be like that:
(x+2)⁶ = 2¹²
=x+2 = 6rooted 2¹²
=x+2 = 2^12/6
=x+2 = 2²
=x+2 = 4
=x =4-2
=x =2
??
Can't it be like that:
(x+2)⁶=2^12
=x+2 = 6 rooted (2)¹²
=x+2 = (2)^12/6
=x+2 = (2)²
=x+2 = 4
=x = 4 -2
=x = 2
Sorry sir, but I have a querie
Can't it be like that:
(x+2)⁶ = 2¹²
=x+2 = 6rooted 2¹²
=x+2 = 2^12/6
=x+2 = 2²
=x+2 = 4
=x =4-2
=x =2
??😅
Sorry sir, but I have a querie
Can't it be like that:
(x+2)⁶ = 2¹²
=x+2 = 6rooted 2¹²
=x+2 = 2^12/6
=x+2 = 2²
=x+2 = 4
=x =4-2
=x =2
??😅
Sorry sir, but I have a querie
Can't it be like that:
(x+2)⁶ = 2¹²
=x+2 = 6rooted 2¹²
=x+2 = 2^12/6
=x+2 = 2²
=x+2 = 4
=x =4-2
=x =2
??😅
Sorry sir, but I have a querie
Can't it be like that:
(x+2)⁶ = 2¹²
=x+2 = 6rooted 2¹²
=x+2 = 2^12/6
=x+2 = 2²
=x+2 = 4
=x =4-2
=x =2
??😅
Sorry sir, but I have a querie
Can't it be like that:
(x+2)⁶ = 2¹²
=x+2 = 6rooted 2¹²
=x+2 = 2^12/6
=x+2 = 2²
=x+2 = 4
=x =4-2
=x =2
??😅
Sorry sir, but I have a querie
Can't it be like that:
(x+2)⁶ = 2¹²
=x+2 = 6rooted 2¹²
=x+2 = 2^12/6
=x+2 = 2²
=x+2 = 4
=x =4-2
=x =2
??😅
You've found one solution. You need to find six roots!