Question

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Answer 1

Question: x = √12 + √12 + √12 +... ∞, then find the value of x.

x = √(12 + √(12 + √(12 +... ∞)))

x = sqrt12 + sqrt12 + sqrt12 +... Infinite

Answer:

4

Step-by-step explanation:

∞ represents largeness without any boundary.

Removing 1 term from an infinite series makes no difference.

Here, x = √(12 + √(12 + √(12 +... ∞)))

So, the bold content '√(12 + √(12 +... ∞))' is also equal to x.

=> x = √(12 + x)

=> x² = (12 + x)

=> x² - x - 12 = 0

=> x² - (4 - 3)x - 12 = 0

=> x² - 4x + 3x - 12 = 0

=> x(x - 4) +3(x - 4) = 0

=> (x - 4)(x + 3) = 0

=> x = 4 or x = -3

Since, terms under square-root can't be negative, x must be +ve → x = 4