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Solving Nested Radical Equation (Posted on 2024-10-22)

Solve for x:

 x + √(x + 1/2 + √(x + 1/4)) = 1024

No Solution Yet Submitted by K Sengupta

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solution

| Comment 1 of 2

Let (x+1/4)=a^2 so that x=a^2-1/4.

Substitute for x and the value under the outer radical becomes (a+1/2)^2 which after simplification turns out to also be the value of LHS: a^2-1/4+a+1/2=(a+1/2)^2.

Take square roots to get a=63/2. Then x=(63/2)^2-1/4=3968/4=992.

Posted by xdog on 2024-10-23 19:43:46

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