Question

Solve algebraically (x + 2)^7/2 = (x + 2)^3/2

Answer 1

(x + 2)^7/2 = (x + 2)^3/2

Subtract (x + 2)^3/2 from each side

(x + 2)^7/2- (x + 2)^3/2=(x + 2)^3/2-(x + 2)^3/2

(x + 2)^7/2- (x + 2)^3/2=0

Factor the expression

(x + 2)^3/2[(x + 2)^2-1]=0

(x + 2)^3/2[(x + 2)^2-1]=0

(x + 2)^3/2[(x + 2+1)(x+2-1)]=0

(x + 2)^3/2[(x +3)(x+1)]=0

x + 2=0

x = -2

x+3 = 0

x=-3

x+1 =0

x = -1

Therefore, the solutions are -1,-2 and -3