Question

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

Answer 1

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 

⇒ x² + x - 56 = 0 

⇒ x² + 8x - 7x - 56 = 0 

⇒ x (x + 8) - 7(x + 8) = 0 

⇒ x = - 8, 7

∴ The value of x = 7