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.

Hana Wehbi by Hana Wehbi , 51, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

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.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...