Q238
If m = 5 + 5 + 5..... and n = 5 - 5 - 5..... then among the following the relation between m & n holds is?
If and 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
AnswerAnswer: Option D
Solution
Answer: Option D
Solution:
\begin{aligned}
& {\text{Let }}m = \sqrt {5 + \sqrt {5 + \sqrt 5 } } \\
& {\text{Factor}} = \left( a \right) \times \left( {a + 1} \right) \\
& {\text{Here }}m = a + 1 \\
& \Rightarrow m - 1 = a\,.........(i) \\
& {\text{Let }}n = \sqrt {5 - \sqrt {5 - \sqrt 5 } } \\
& {\text{Factor}} = \left( a \right) \times \left( {a + 1} \right) \\
& {\text{Here }}n = a\,.........(ii) \\
& {\text{From (i) & (ii)}} \\
& \Leftrightarrow m - 1 = n \\
& \Leftrightarrow m - n - 1 = 0 \\\end{aligned}