Prove that for no integer n, n6 +3n5_5n4_15n3+4n2+12n+3 is a perfect square.
Prove that for no integer n, n6 +3n5_5n4_15n3+4n2+12n+3 is a perfect square.
Ahalya , 11 Years ago
Grade 10
10 grade maths> Prove that for no integer n, n 6 +3n 5_ 5...
1 Answers
Nishant Vora
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
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
Approved Last Activity: 11 Years ago
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