更新1:
Can someone give some explanation to their answers. ie why the answer is blah blah blah etc.
Evaluate √(3+√(3+√(3…)) )?
回答 (3)
2009-04-17 11:21 am
✔ 最佳答案
√{3 + √[3 + (√3 + √3 ...)]} Let x = √{3 + √[3 + (√3 + √3 ...)]}
√{3 + √[3 + (√3 + √3 ...)]} = √(3 + x)
x = √(3 + x)
x^2 = 3 + x
x^2 - x - 3 = 0
x = [-b ±√(b^2 - 4ac)]/2a
a = 1
b = -1
c = -3
x = [1 ±√(1 + 12)]/2
x = [1 ±√13]/2
∴ x = [1 ±√13]/2
2009-04-17 10:19 am
Let the expression be x so Rt(x+3) = x or x^2 = x+3
Now solve x^2 - x - 3 = 0 and take the root tht is +ve.
Now solve x^2 - x - 3 = 0 and take the root tht is +ve.
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