Math, asked by nase69, 9 months ago

» 22
 \sqrt{8 + 2 \sqrt{8 + 2 \sqrt{8........... \infty } } }

Answers

Answered by abhi569
2

Answer:

4

Step-by-step explanation:

⇒ √[ 8 + 2√{ 8 + 2√( 8 ... ∞

Let this be equal to a.

⇒ √[ 8 + 2√{ 8 + 2√( 8 ... ∞ = a

⇒ 2√[ 8 + 2√{ 8 + 2√( 8 ... ∞ = 2a

⇒ 2√( 8 + 2a ) = 2a                   { √[ 8 + 2√{ 8 + 2√( 8 ... ∞ = a }

4( 8 + 2a ) = 4a^2

32 + 8a = 4a^2

4a^2 - 8a - 32 = 0

a^2 - 2a - 8 = 0

⇒ a^2 - ( 4 - 2 )a - 8 = 0

⇒ a^2 - 4a + 2a - 8 = 0

⇒ a( a - 4 ) + 2( a - 4 ) = 0

⇒ ( a - 4 )( a + 2 ) = 0

⇒ a = 4   or   a = - 2

⇒ a = 4     { a ≠ -ve }

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