Question

If x=√2+√2+√2.....then x=?​

Answer 1

value of x = 2

I think your question is....

if x = √{2 + √{2 + √{2 + ........}}} then we have to find value of x.

√{2 + √{2 ........}} = x

[ there are infinite terms in the given expression. removing or adding one finite term into it, doesn't change its value. so, √{2 + √{2 ........}} = x also ]

now, x = √{2 + x}

now squaring both sides we get,

x² = 2 + x

x² - x - 2 = 0

x² - 2x + x - 2 = 0

x(x - 2) + 1(x - 2) = 0

(x + 1)(x - 2) = 0

x = 2, -1

but x = √{2 + √{2 + √{2 ........}} > 0

so, x ≠ -1 and hence x = 2

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