The correct option is D 3Given, √(6+√(6+√(6+......∞))) let, x=√(6+......∞) x^2=6+√(6+√(6+√(6+......∞))) x^2=6+x x^2 x 6=0 (x 3)(x+2 ...

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Standard XII

Mathematics

Quadratic Formula for Finding Roots

√6+√6+√6+.......

Question

$\sqrt{6 + \sqrt{6 + \sqrt{6 + . . . . . . . . . \infty}}}$ is:

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3.5

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Solution

The correct option is D 3
Given,

$\sqrt{6 + \sqrt{6 + \sqrt{6 + . . . . . . \infty}}}$

let,

$x = \sqrt{6 + . . . . . . \infty}$

$x^{2} = 6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + . . . . . . \infty}}}$

$x^{2} = 6 + x$

$x^{2} - x - 6 = 0$

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

$x = 3$

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Similar questions

If $\frac{6^{6} + 6^{6} + 6^{6} + 6^{6} + 6^{6} + 6^{6}}{3^{6} + 3^{6} + 3^{6}} \div \frac{4^{6} + 4^{6} + 4^{6} + 4^{6}}{2^{6} + 2^{6}} = 2^{n}$ then find the value of $n$ .

Mark the correct option:

The number is equal to

A. 6⁶

\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + . . .}}}}

up to

\infty

is?

Q. Find the value of

^{6} C_{0} .^{12} C_{6} -^{6} C_{1} .^{11} C_{6} +^{6} C_{2} .^{10} C_{6} +^{6} C_{2} .^{10} C_{6} -^{6} C_{3} .^{9} C_{6} +^{6} C_{4} .^{8} C_{6} -^{6} C_{5} .^{7} C_{6} +^{6} C_{6} .^{6} C_{6}

\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + . . . .}}}}

= ?

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√6+√6+√6+.........∞ is:

The correct option is D 3Given,√6+√6+√6+......∞let,x=√6+......∞x2=6+√6+√6+√6+......∞x2=6+xx2−x−6=0(x−3)(x+2)=0x=3

$\sqrt{6 + \sqrt{6 + \sqrt{6 + . . . . . . . . . \infty}}}$ is:

The correct option is D 3
Given,

$\sqrt{6 + \sqrt{6 + \sqrt{6 + . . . . . . \infty}}}$

let,

$x = \sqrt{6 + . . . . . . \infty}$

$x^{2} = 6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + . . . . . . \infty}}}$

$x^{2} = 6 + x$

$x^{2} - x - 6 = 0$

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

$x = 3$