CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If the product of four consecutive natural numbers increased by a natural number ρ is a perfect square, then the value of ρ is:

A
8
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 1
Let the four consecutive natural numbers be x,(x+1),(x+2),(x+3).
Now, x(x+1)(x+2)(x+3)+p=x(x+3)(x+1)(x+2)+p
=(x2+3x)(x2+3x+2)+p
=(x2+3x)2+2(x2+3x)+p
Given that this is a perfect square, the value of p=1, so that the above
equation becomes (x2+3x)2+2(x2+3x)+1=(x2+3x+1)2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Interesting Patterns
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon