What's b?

Algebra Level 2

If a = b + b + b + b + . . . a=\sqrt{b+\sqrt{b+\sqrt{b+\sqrt{b+...}}}}

What's b ?

  • The sum continues to infinity.
  • a > 1 a>1 .
b = a 2 + a b=a^2 + a b = a b=a b = a 2 − a b=a^2 - a b = a 2 b=a^2

Abd Fml<3 by Abd FmL<3 , 19, France

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1 solution

Abd Fml<3
Jan 24, 2019

a = b + b + b + b + . . . a=\sqrt{b+\sqrt{b+\sqrt{b+\sqrt{b+...}}}}

Replace : a = b + a a=\sqrt{b+a}

Then square both sides : a 2 = b + a a^2 = b+a

Rearrange : a 2 − a = b a^2 - a = b

1 Helpful 1 Interesting 0 Brilliant 0 Confused

Mais wi c’est claii

Jules Battaglia - 2 years, 4 months ago

T'a compris ? 😂

Abd FmL<3 - 2 years, 4 months ago

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