Question

HOLA BRAINLIACS♥♥♥
I'M HERE WITH MY BRAINLY QUES
(ONLY REAL GENIUS WOULD BE ABLE TO SOLVE THIS!!!!!)


$if \: x = \sqrt{ 6 + \sqrt{ 6 +\sqrt{6 + .....} } } \infty \\ find \: x \: where \: is \: a \: natural \: number$
HOPING TO GET RIGHT ANSWER...☺☺☺

Answer 1

Wow, this is one of a kind sums which are usually found in the Olympiad exams !

So,
x= √6+√6+√6 +... which goes onto infinity

So now,
Squaring both sides,

x^2 = 6 + √6+√6+√6+....
So,
x^2 = 6 + x
x^2 - x + 6 = 0
(x-3)(x+2) = 0

So,
Since x is a natural number,
Therefore,

x = 3

Answer 2

Answer:

Wow, this is one of a kind sums which are usually found in the Olympiad exams !

So,

x= √6+√6+√6 +... which goes onto infinity

So now,

Squaring both sides,

x^2 = 6 + √6+√6+√6+....

So,

x^2 = 6 + x

x^2 - x + 6 = 0

(x-3)(x+2) = 0

So,

Since x is a natural number,

Therefore,

x = 3