SOLUTION: solve in R: x= 12-sqrt(12-sqrt(x))

Algebra ->  Graphs -> SOLUTION: solve in R: x= 12-sqrt(12-sqrt(x))      Log On


   



Question 1121373: solve in R: x= 12-sqrt(12-sqrt(x))
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x=+12-sqrt%2812-sqrt%28x%29%29
x-+12=sqrt%2812-sqrt%28x%29%29 .......square both sides
%28x-+12%29%5E2=%28sqrt%2812-sqrt%28x%29%29%29%5E2
x%5E2-+24x%2B144=+12-sqrt%28x%29
x%5E2-+24x%2B144-12=+-sqrt%28x%29
x%5E2-+24x%2B132=+-sqrt%28x%29 .....square both sides
%28x%5E2-+24x%2B132%29%5E2=+%28-sqrt%28x%29+%29%5E2
x%5E4+-+48+x%5E3+%2B+840+x%5E2+-+6336+x+%2B+17424=x
x^4 - 48 x^3 + 840 x^2 - 6336 x-x + 17424=0
x%5E4+-+48+x%5E3+%2B+840+x%5E2+-+6337+x+%2B+17424=0
solutions:
x=9
x=16
x=%2823%2B3sqrt%285%29%29%2F2
x=%2823-3sqrt%285%29%29%2F2

if you verify solutions, you will notice that only x=9 will make +x=+12-sqrt%2812-sqrt%28x%29%29 true