Re: If the following expression extends to an infinite number of roots, th
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03 Mar 2020, 01:32
If x=√{4-√(4+...)}, then x=√{4-√(4+x)}.
From the equation above, x is obviously a positive that must not be greater than 2. Options (B),(C),(E) all show that the value of x is greater than 2, contradicting the logic. Thus, confidently eliminate options (B),(C), and (E).
x = √{4-√(4+x)}
x^2 = 4-√(4+x)
√(4+x) = 4-x^2
4+x= (4-x^2)^2
x= (x^2-4)^2 -4
TRY (A) x = (-1+√13)/2
--> x = ((-1+√13)^2/4 -4)^2 -4
--> x = {-(1+√13)/2}^2 -4
--> x = (1+√13)^2/4 -4
--> x = (14+2√13)/4 -4
--> x = (-1+√13)/2 (CORRECT)
Since (A) is correct, we don't have to check (D). For exercise, you can try to validate (D)
FINAL ANSWER IS (A)
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