SOLUTION: Find x, x + √{(x - ½) + √(x + ¼)} = 1024

Question 1206468: Find x,
x + √{(x - ½) + √(x + ¼)} = 1024
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

using calculator we get

= >will not work ()
= >will not work ()
= >will not work ()

verifying solutions shows that only works

=>true
so, answer is

Answer by ikleyn(53222) (Show Source): You can put this solution on YOUR website!
.

Go to web-site https://www.wolframalpha.com/widgets/gallery/view.jsp?id=b858339e64fa997454dd12f77cb1ece1 (wolfram alpha zeros calculator). Print your expression for the function x + sqrt((x-0.5)+sqrt(x+0.25))-1024, which represents f(x) = and click the "Submit" button. So, you want to get an approximation solution to this equation f(x) = 0. You will get the number x = 992.02, which is really a good approximation to the solution. CHECK. f(992.02) = 1024.005... f(992) = 1023.984...

What I want to say at the end, is THIS: there is no Algebra method/methods
for finding/searching exact solution/solutions to this equation.

There are numerical methods, instead, that provide approximate solution.

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