Nice Algebra Simplification Math Problem || Math Olympiad Question || Olympiad Question Practice

Nice Algebra Simplification Math Problem || Math Olympiad Question || Olympiad Question Practice
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[@haroldlake1005]

(a + b) (a - b) = (7 + 0) (7 - 0) then (a + b) = 7 and (a - b) = 7 then (a + b) + ( a - b) = 7 + 7 then 2a = 14 then a = 7. In the same way: (a + b) - (a - b) = 7 then 2b = 0 then b = 0. The answer is: a = 7 and b = 0 . Which is the mistake ?

[@oleglevchenko907]

No mistake! (7;0) is also a solution. Furthermore, in total there are 6 solutions, as (a-b)*(a+b)= 49 = 1*49=49*1=(-1)*(-49)=(-49)*(-1)=7*7=(-7)*(-7) - there are 6 variants of factorization, and 6 pairs of equations: 1) a+b=1; a-b=49 2) a+b= -1; a-b= -49 3) a+b=49; a-b=1 4) a+b= -49; a-b= -1 5) a+b=7; a-b=7 6) a+b= -7; a-b= -7 By solving these 6 pairs, you will get all 6 solutions: (7;0), (-7;0), (25; 24), (-25; -24), (-25; 24); (25; -24).

[@haroldlake1005]

@@oleglevchenko907 Thank you very much !

[@vikasheda2091]

​@@oleglevchenko907 I have also brought a=7, b=0

[@vikasheda2091]

A=7, b=0 Can be satisfied answer

[@吳昶霖]

（a+b)(a-b)=49 49=7×7=(-7)×(-7) =(1×49)=(-1)(-49) 則a、b可能是 ；-7、0 7、0 或 25、24 -25、-24 -25、24 25、-24

[@oleglevchenko907]

and where are answers for 7*7 and (-7)*(-7)? and what about a+b=1; a-b=49 ? and a+b= -1; a-b= -49 ? You have found 2 solutions, and lost 4 ones...

[@andretewem3385]

Il y a 4 autres solutions : (-7,0), (7,0), (-25,24), (25,-24)

[@mehranhosseini4355]

25 v 24