Daffodil International University

Educational => Mathematics => Math Helps => Topic started by: msu_math on November 21, 2012, 10:52:19 AM

Title: Completing Perfect Squares
Post by: msu_math on November 21, 2012, 10:52:19 AM

Problem: For what integer value n is n² + 6x + 10 also a perfect square?

Solution: Let us first express the given polynomial n² + 6x + 10 in the form "a perfect square + constant". We have, n² + 6x + 10 = (n+3)² +1. If n² + 6x + 10 = m² for some integer m, then 1 = m² - (n+3)². The left hand side gives the difference of two perfect squares which is 1 as in the right side. The only perfect squares that differ by 1 are 0 and 1. Hence, (n+3)² = 0 , having the solution n = -3 which gives the required value of n.

Title: Re: Completing Perfect Squares
Post by: Nargis Akter on April 08, 2017, 01:58:49 PM

Thanks