Find the value of square root of 6 plus square root of 6 plus square root of 6 plus end root end root end root midline horizontal ellipsis

Asked by Gopinath | 17th Mar, 2017, 10:10: PM

Expert Answer:

begin mathsize 16px style Let space straight x equals space square root of 6 plus square root of 6 plus square root of 6 plus.... end root.... end root end root
Squaring space both space sides
rightwards double arrow straight x squared equals 6 plus square root of 6 plus square root of 6 plus.... end root.... end root
rightwards double arrow straight x squared equals 6 plus straight x
rightwards double arrow straight x squared minus straight x minus 6 equals 0
rightwards double arrow left parenthesis straight x minus 3 right parenthesis left parenthesis straight x plus 2 right parenthesis equals 0
rightwards double arrow straight x minus 3 equals 0 space or space straight x plus 2 equals 0
rightwards double arrow straight x equals 3 space or space straight x equals negative 2
rightwards double arrow square root of 6 plus square root of 6 plus square root of 6 plus.... end root.... end root end root equals 3 space or space square root of 6 plus square root of 6 plus square root of 6 plus.... end root.... end root end root equals negative 2
But space straight x space can space only space be space straight a space positve space real space number comma space since space we space cannot space take space root space of space straight a space negative space number
in space real space numbers.
Hence comma space straight x equals 3 rightwards double arrow square root of 6 plus square root of 6 plus square root of 6 plus.... end root.... end root end root equals 3 end style

Answered by Rebecca Fernandes | 17th Mar, 2017, 10:42: PM