Question

solve this question​

Answer 1

Step-by-step explanation:

y=-2(not possible)

y use

Answer 2

Answer:

$\bf\ your \: answer \\ \\ \bf\\: y = - 2(not \: possible) \: and \:y = 3$

Step-by-step explanation:

$\bf\ \: \sqrt{ 6 + \sqrt{6 + \sqrt{6 + ................ .........\infty } } } \\ \\ \bf\ \: let \: \: \: \sqrt{6 + \sqrt{6 + \sqrt{6} } } = y \\ \\ \sf\ \therefore \sqrt{6 + y} = y \\ \\ \sf\ \implies: 6 + y = {y}^{2} \\ \\ \sf\ \implies: {y}^{2} - y - 6 = 0 \\ \\ \sf\ \implies: {y}^{2} - (3y - 2y) - 6 = 0 \\ \\ \sf\ \implies: {y}^{2} - 3y + 2y - 6 = 0 \\ \\ \sf\ \implies:y(y - 3) + 2(y - 3) = 0 \\ \\ \sf\boxed{ \sf\implies:(y - 3)(y + 2) = 0} \\ \\ \\ \sf\ y - 3 = 0 \\ \\ \sf\ \implies:y = 3 \\ \\ \sf\boxed{ \implies: \sqrt{6 + \sqrt{6 + \sqrt{6 + ................ + \infty } } } = 3 }\\ \\ \bf\huge\red{or} \\ \\ \sf\ y + 2 = 0 \\ \\ \sf\ \implies:y = - 2 \\ \\ \sf\boxed{ \implies: \sqrt{6 + \sqrt{6 + \sqrt{6 + .................. + \infty } } = - 2(not \: possible)}}$