i need to solve √z+1 + √2z+3= 1

Question

z+1 and 2z+3 are both under the radical

 

*im lost, i need help preferably step by step*

Answer 1

Isolate one of the radicals:

 

√(z+1) = 1 - √(2z+3)

 

Square both sides to get:  z+1 = 1 - 2√(2z+3) + (2z+3)

 

Isolate the remaining radical:

 

   2√(2z+3) = z +3

 

Square both sides to obtain:  4(2z+3) = z² + 6z + 9

 

    z² - 2z - 3 = 0

 

   (z-3)(z+1) = 0

 

   z = 3 or z = -1

 

Check each value in the original equation:  -1 works, but 3 doesn't

 

Solution:  -1