Find the value of \sqrt{30 +\sqrt{30 +\sqrt{30 +\sqrt30}.... }

RRB Non Technical Model Papers 8 with solutions

Question : 37 of 100

Marks: +1, -0

Find the value of

√{30 +√{30 +√{30 +√30}}.... }

Solution:

√{30 +√ {30 + √{30 +√ 30}}}.... = x

⇒√ {30 + x }= x⇒x^2 = 30 + x

⇒

x^2 – x – 30 = 0

⇒x^2 –6 x + 5x – 30 = 0

⇒ x (x - 6) +5(x - 6) = 0

⇒ (x + 5)(x - 6) = 0

⇒ x + 5 = 0 or x-6 = 0 x = -5

(ignore) or x = 6 The answer is x = 6

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