Question

please help me with this​

Answer 1

Question : -

The value of √(6+√(6+√(6+ .........∞))) is

• [A] 4
• [B] -2
• [C] 3
• [D] 3.5

ANSWER

Required to find : -

• The value of √(6+√(6+√(6+ .........∞))) ?

Formula used : -

Quadratic formula;

x = ( -b±√[b²-4ac])/(2a)

Solution : -

The value of √(6+√(6+√(6+ .........∞)))

So,

Let,

x = √(6+√(6+√(6+ .........∞))) .......{1} equation-1

Consider Equation 1

x = √(6+√(6+√(6+ .........∞)))

squaring on both sides

(x)² = [√(6+√(6+√(6+ .........∞)))]²

x² = 6+√(6+√(6+ .........∞))

x² = 6+x [ from equation-1 ]

{ since, x = √(6+√(6+√(6+ .........∞)))}

x²-x-6=0

Now,

We need to solve this quadratic equation using the quadratic formula.

The standard form of the quadratic equation is ax²+bx+c=0.

Comparing the standard form with the above quadratic equation;

ax²+bx+c=0 & x²-x-6=0

Here,

• a=1
• b=-1
• c=-6

This implies;

x = ( -b±√[b²-4ac])/(2a)

x = (-{-1}±√[{-1}²-4{1}{-6}])/(2{1})

x = (1±√[1+24])/(2)

x = (1±√[25])/(2)

x = (1±5)/(2)

x = (1+5)/(2) (or) (1-5)/(2)

x = (6)/2 (or) (-4)/(2)

x = 3 (or) -2

since,

A negative number can't be under a root if so it becomes as an imaginary number .

so,

x = 3

Hence,

value of √(6+√(6+√(6+ .........∞))) = 3

option-c is correct ✓