this question comes from the words problems Nov 7 | Galeboe from New York, NY | 3 Answers | 0 Votes Mark favorite Subscribe Comment
a+b=5 a^{2}-b^{2}=45 a^{2}-b^{2}=(a+b)(a-b)=5(a-b)=45 a+b=5 a -b=9 add them 2a=14 so a=7 subtract them 2b=-4 b=-2 Nov 7 | Michael F. Comment
a+b=5 a^{2}-b^{2}=45 System of non-linear equations: (two unknowns in two equations) Solve by iterative substitution. b = 5-a a^{2}-(5-a)^{2}=45 a^{2}-(25-10a+a^{2}) = 45 10a-25=45 10a=70 a=7 b=5-a b=5-7 b=-2 Nov 7 | Timothy S. Comment
just a thought looking at the problem; what perfect square is close to 45 ? 49 !!! 49-45=4, another perfect square(2x2) looking at 7 and 2, their sum is not 5, but 7 and -2 have a sum of 5 (7^2)-(-2)^2=49-4=45 and 7+(-2)=5 Nov 7 | Arthur D. Comment