# $x=\sqrt{(\{56)-\sqrt{([56)-\sqrt{((56)...\infty)]}\}}}$. Find the value of X.

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$x=\sqrt{(\{56)-\sqrt{([56)-\sqrt{((56)...\infty)]}\}}}$. Find the value of X.
1. 5
2. 6
3. 7
4. 8

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Correct Answer - Option 3 : 7

Given,

The expression

$x=√{(\{56)-√{([56)-√{((56)...\infty)]}\}}}$

Calculation

$x=√{(\{56)-√{([56)-√{((56)...\infty)]}\}}}$

⇒  x = √ 56  - x  (let the x remaining expression)

Squaring both sides,

x2  = 56 - x

⇒ x+ x - 56 = 0

⇒ x2 + 8x - 7x - 56 = 0

⇒ x (x + 8) - 7(x + 8) = 0

⇒ x = - 8, 7

∴ The value of x = 7