Show that P+1+P+1+P...1 1 2=P2+4P

P+1+P+1+P...1 1 2=x [say](x−p)=1+(P+x) /21 2⇒(x−p)=2+P+x2(P+x) ⇒(x−p)(p+x+2)=2P+2x⇒Px+x2+2x−P2−Px−2P=2P+2x⇒x2=P2+4P⇒x=P2+4P

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Show that P+ { 2 }{ 1+ { 1 }{ P+ { 1 }{ 1+P... } } } ={P^2+4

Question

Show that $P + \frac{2}{1 + \frac{1}{P + \frac{1}{1 + P ...}}} = P^{2} + 4 P$

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Show that

P + \frac{2}{1 + \frac{1}{P + \frac{1}{1 + P ...}}} = P^{2} + 4 P

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P + \frac{2}{1 + \frac{1}{P + \frac{1}{1 + P ...}}} = x

[say]

(x - p) = \frac{2}{1 + \frac{1}{( P + x ) / 2}}

\Rightarrow (x - p) = \frac{2 ( P + x )}{2 + P + x}

\Rightarrow (x - p) (p + x + 2) = 2 P + 2 x

\Rightarrow P x + x^{2} + 2 x - P^{2} - P x - 2 P = 2 P + 2 x

\Rightarrow x^{2} = P^{2} + 4 P

\Rightarrow x = P^{2} + 4 P

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Question Text	Show that $P + \frac{2}{1 + \frac{1}{P + \frac{1}{1 + P ...}}} = P^{2} + 4 P$
Answer Type	Text solution:1
Upvotes	150