What is a + b = ? a+b=?

Calculus Level 3

Given: a = 6 + 6 + 6 + a=\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{\dots}}}} and b = 20 20 20 b=\sqrt{20-\sqrt{20-\sqrt{20-\sqrt{\dots}}}}

What is a + b ? a+b?


The answer is 7.

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1 solution

Hana Wehbi
Jul 30, 2018

a = 6 + 6 + 6 + a 2 a 6 = 0 ( a 3 ) ( a + 2 ) = 0 a = 3 we only take the positive value. a=\sqrt{6+\sqrt{6+\sqrt{6+\sqrt{\dots}}}}\implies a^2-a-6=0\implies (a-3)(a+2)=0\implies a=3\text{ we only take the positive value.} and b = 20 20 20 b 2 + b 20 = 0 ( b + 5 ) ( b 4 ) = 0 b = 4 because b= -5 is not acceptable. b=\sqrt{20-\sqrt{20-\sqrt{20-\sqrt{\dots}}}}\implies b^2+b-20=0\implies (b+5)(b-4)=0\implies b=4\text{ because b= -5 is not acceptable.}

Therefore, a + b = 3 + 4 = 7. a+b=3+4=7.

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