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

SSC CPO SI and ASI Model Paper 1

Question : 111 of 200

Marks: +1, -0

Find our the value of ${√{√30+√ 30 +√ 30+√ 30....} }$

Solution:

(3) Let

√{30 +√ 30 +√30+ √30.... }= x

⇒√{ 30+x} = x

⇒x^2 = 30 + x

⇒x^2– x – 30 = 0

⇒x(x –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 = 6The answer is x = 6

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