$$\eqalign{
& {\text{If m}} = \sqrt {5 + \sqrt {5 + \sqrt {5\,......} } } \cr
& {\text{n}} = \sqrt {5 - \sqrt {5 - \sqrt {5\,......} } } \cr} $$
then among the following the relation between m & n holds is.
A. m - n + 1 = 0
B. m + n + 1 = 0
C. m + n - 1 = 0
D. m - n - 1 = 0
Answer: Option D
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let m}} = \sqrt {5 + \sqrt {5 + \sqrt 5 } } \cr & {\text{Factor}} = \left( a \right) \times \left( {a + 1} \right) \cr & {\text{Here m}} = a + 1 \cr & {\text{or m}} - 1 = a\,.\,.\,.\,.\,.\,.\,.\,.\,.\,\left( {\text{i}} \right) \cr & {\text{Let n}} = \sqrt {5 - \sqrt {5 - \sqrt 5 } } \cr & {\text{Factor}} = \left( a \right) \times \left( {a + 1} \right) \cr & {\text{Here n}} = a\,.\,.\,.\,.\,.\,.\,.\,.\,.\,\left( {{\text{ii}}} \right) \cr & {\text{From equation}}\left( {\text{i}} \right){\text{ and }}\left( {{\text{ii}}} \right) \cr & {\text{m}} - 1 = {\text{n}} \cr & {\text{or m}} - {\text{n}} - 1 = 0 \cr} $$Related Questions on Surds and Indices
A. $$\frac{1}{2}$$
B. 1
C. 2
D. $$\frac{7}{2}$$
Given that 100.48 = x, 100.70 = y and xz = y2, then the value of z is close to:
A. 1.45
B. 1.88
C. 2.9
D. 3.7
Join The Discussion