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40. Solve for \( x \), if \( x=\frac{1}{2+\frac{1}{2+\frac{1}{2+\cdots \infty}}} \) |
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Answer» \(x = {1\over 2+ \frac{1} {2+ \frac{1}{2 ....∞}}}\) \(→ x = {1\over 2+x}\) \(→x^2+2x=1 \) \(→x^2+2x-1=0\) → \(x = {-2 \pm \sqrt{2²-4(1)(-1)} \over 2(1)}\). →\(x = {-2 \pm \sqrt{8} \over 2}\) →\(x = {-2 \pm 2\sqrt{2} \over 2}\) \(→x = {-1 \pm \sqrt{2} }\) |
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