Question

please help me.....​

Answer 1

Given:

• $\sf{\sqrt{6+\sqrt{6+\sqrt{6.....}}}}$

To Find:

• Its value.

Answer :

Let us take $\sf{\sqrt{6+\sqrt{6+\sqrt{6.....}}}}$ = x .

=> x = $\sf{\sqrt{6+\sqrt{6+\sqrt{6.....}}}}$

=> x = $\sf{\sqrt{6+x}}$

=> x² = 6 + x .

=> x²-x-6=0.

=> x²-3x+2x-6=0.

=> x(x-3)+2(x-3) = 0.

=> (x-3)(x+2) = 0.

=> x = 3,-2.

Since x can't be -ve .

Hence the required answer is 3.