Suppose n is a positive integer such that n2 48 is a perfect square What is the number of such n ........

Quantitative Aptitude (CDS) Number System

Download Solution PDF

Suppose n is a positive integer such that (n² + 48) is a perfect square. What is the number of such n?

One

Two

Three

Four

छोटे Courses बड़े Results

Master Number System

Prepare through Micro-courses

Try Now

Explanation:

N²+ 48 =k²
48 =k² – N²
(k - N)(k + N) = 48
So the possible number of pairs of (k - N) and (k + N) are
(1,48),(2,24), (3,16), (4,12), (6,8)
On solving the above pairs for (k - N) and (k + N), we get the integer values of N and k as
N=4 , k=8
N=11,k=13
So the total possible values of N are three.