Question

√a+b=11 and √b+a =7 find the value of a and b

Answer 1

see, this can be solved logically. root(a)+b and root(b)+a , both are integers. So both a and b are perfect squares, and both are less than 11 and 7, why... because they are positive integers and so each of a and b is less than the value obtained when something positive is added to a and b. So the perfect squares less than 11 and 7 are 4,9,1... if we take any of a or b as 1, then other variable doesnt give perfect square upon solving. so a and b are 4 and 9