# mathematics #matholympiad | a^2 + b=73, b^2+a =73, solve for a and b

Hello friends in this video, we are going to discuss an algebraic equation solve for a B if a square plus B equal to 73 B square plus a equal to 73 With the condition a not equal to B now to solve this equation. We are going to Subtract 2 from 1 and we have a square plus B minus B square plus a Equal to 73 minus 73 By opening the brackets. We have a square plus B This minus is multiplied with the brackets and we have minus B square minus a equal to 73 minus 7 3 equal to 0 now Gathering the similar term a square with minus B square and B with minus a Taking the factors of a square minus B square a minus B a plus B B minus a can be written in the form of minus times a minus B equal to 0 Now we can observe that a minus B is a common factor between two terms so we can take out from this two terms and we have a minus B a plus B and minus 1 we have property Multiplication of two number is 0 that one of the number must be 0 therefore we have a minus B equal to 0 or a plus B minus 1 equal to If we simplify then we have a equal to B and a plus B equal to 1 but we have given that a Not equal to B. That means a equal to B is not possible hence, we have a plus B equal to 1 now from this equation a plus B equal to 1 we can write down B equal to 1 minus a substitute that value in equation 1 then we have a Square B equal to 1 minus a equal to 73 now simplify Then we have a square minus a plus 1 minus 73 equal to 0 1 minus 73 equal to minus 72 therefore we have a square minus a minus 72 equal to 0 it is a quadratic equation and We want to find the roots of this equation For that we have to find the factors of 72 whose subtraction is Minus 1 and the factors are 9 Into 8 equal to 72 so 9 and 8 are the factor so we can rewrite the equation a square minus 9 a plus 8 a minus 72 equal to 0 a Is a common factor in first two terms and 8 is a common factor in the last two terms Therefore we have a minus 9 and a plus 8 equal to 0 with the similar property Multiplication of two number is 0 then one of the number must be 0 therefore we have a minus 9 equal to 0 or a plus 8 equal to If a minus 9 equal to 0 then a equal to 9 and a plus 8 equal to 0 then a equal to minus 8 suppose a equal to 9 then B equal to 1 minus a equal to 1 minus 9 equal to minus 8 therefore B equal to minus 8 if A equal to 9 then B equal to minus 8 Suppose a equal to minus 8 and B equal to 1 minus a equal to 1 minus Minus 8 minus minus plus so we have 1 plus 8 equal to 9 Therefore be equal to that means a equal to minus 8 then B equal to Therefore we had two possible solution of the equation a square plus B equal to 73 and B square plus a equal to 73 Are a equal to 9 and B equal to minus 8 or a equal to minus 8 and B equal to Thanks for watching for more videos like share subscribe place the bail icon of next gen