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find the value of √6+√6+√6+......infinity

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find the value of √6+√6+√6+......infinity

Posted by Anshika Dixit 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Let {tex}x = \sqrt { 6 + \sqrt { 6 + \sqrt { 6 + \dots } } }{/tex} ......(i)
{tex}\Rightarrow{/tex} x² = {tex}( \sqrt { 6 + \sqrt { 6 + \sqrt { 6 . . } } } ) ^ { 2 }{/tex} [Squaring both sides]
{tex}\Rightarrow{/tex} x² = {tex}6 + \sqrt { 6 + \sqrt { 6 + \sqrt { 6 + \ldots } } }{/tex}
{tex}\Rightarrow{/tex} {tex}x^2 = 6 + x{/tex} [From (i)]
{tex}\Rightarrow{/tex} {tex}x^2 - x - 6 = 0{/tex}
{tex}\Rightarrow{/tex} {tex}(x - 3) (x + 2) = 0{/tex}
{tex}\Rightarrow{/tex} {tex}x = 3, x = -2{/tex}
{tex}\therefore{/tex} x = 3 [{tex}\because{/tex} x > 0]

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Posted by Kanika . 1 month ago

CBSE > Class 10 > Mathematics

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Don't post personal information, mobile numbers and other details.
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Posted by Hari Anand 6 months, 1 week ago

CBSE > Class 10 > Mathematics