Find all values of x

Question

If g(x)=(x+2/3)² , find all values of x for which g(x)= 25/9

 

Express complex numbers in terms of i. Simplify the answer.

 

list all such values of x 

Answer 1

g(x) = (x + 2/3)² 

 

(x + 2/3)² = 25/9

 

√(x+ 2/3)² = √(25/9)

 

x + 2/3 = ±5/3

 

x = -7/3 and 1

 

Check:

g(x)  = (x + 2/3)²

g(1)  = (1 + 2/3)²

= (5/3)2

= 25/9

g(-7/3) = (-7/3) + 2/3)²

    = (-5/3)²

    = 25/9

Check!