0

Guest

Courses New

Prove that for no integer n, n 6 +3n 5_ 5n 4_ 15n 3 +4n 2 +12n+3 is a perfect square.

Prove that for no integer n, n6  +3n5_5n4_15n3+4n2+12n+3 is a perfect square.

Grade:10

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
9 years ago
Hello Student
Please fidn the soln

n6 +3n5_5n4_15n3+4n2+12n+3 =
= n5(n+3) –5n3(n+3)+4n(n+3) + 3
=(n+3)[n5 –5n3+4n] + 3
=n(n+3)[n4-5n2+4] + 3
=n(n+3)(n2-4)(n2-1) + 3
=(n-2)(n-1)n(n+1)(n+2)(n+3) + 3

So this can not be perfect square

Thansk

Think You Can Provide A Better Answer ?

Other Related Questions on 10 grade maths

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More