Solve (r^4-1)/(r^2-1)=10

Question

This is from the chapter geometric progression. ...

Answer 1

 

(r4−1)(r2−1)=10

 

(r2)2−12r2−12=10

 

(r2−1)(r2+1)(r−1)(r+1)=10

 

Answer: r ∈ {3,(−3)}

Answer 2

r^4-1=(r^2-1)(r^2+1), so (r^4-1)/(r^2-1)=r^2+1=10, so r^2=9 and r=±3,

Answer 3

(r^4-1)/(r^2-1)=10

r^4-1 = 10(r^2-1)

r^4-1 = 10r^2-10

(r^2-5)^2 = 16

r^2-5 = √16

r^2-5 = ±4

r^2=9 or r^2=1

r=±3 or r=±1

Geometric Progression