Question

Radical din x+16 + radical din 1-x=5

Answer 1

√(x+16)+√(1-x) = 5 

 √(x+16) = a,  √(1-x) = b 

 a+b = 5
 a^2+b^2 = x+16+1-x = 17 

a+b = 5 
(a+b)^2 - 2ab = 17

a+b = 5 
5^2 - 2ab = 17

a+b = 5
2ab = 25-17 = 8

a+b = 5
ab = 8:2

a+b = 5 = S
ab = 4 = P

t²-St+P = 0 => t²-5t+4 = 0  => t²-t-4t+4 = 0 => t(t-1)-4(t-1) = 0 =>
=> (t-1)(t-4) = 0 

t = 1 => a = 1 => √(x+16) = 1 => x + 16 =1 => x = -15
t = 1 => b = 1 => √(1-x) = 1 => 1-x = 1 => x = 0

t = 4 => a = 4 => √(x+16) = 4 => x+16 = 4² => x = 0
t = 4 => b = 4 => √(1-x) = 4 => 1-x = 16 => x = -15

=> S = {-15; 0}