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TS EAMCET · Maths · Quadratic Equation

The value of \(\sqrt{42+\sqrt{42+\sqrt{42+\ldots \ldots .}}}\) is equal

  1. A \(7\)
  2. B \(-6\)
  3. C \(5\)
  4. D \(4\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(7\)

Step-by-step Solution

Detailed explanation

Let \(y=\sqrt{42+\sqrt{42+\sqrt{42+\ldots}}}\) \[ \Rightarrow \quad y=\sqrt{42+y} \] On squaring both sides, we get \[ \begin{aligned} & y^2=42+y \\ & \Rightarrow \quad y^2-y-42=0 \\ & \end{aligned} \]…