Question

the sum of two numbers is 1000. the difference between their squares is 256000. find the numbers

Answer 1

let the numbers be x and y according to question x+y=1000..........(1) also, it is given that x^2-y^2=256000. using the identity a^2-b^2= (a+b)(a-b) we get (x+y)(x-y)= 256000 using equation 1 we get 1000(x-y)=256000 on further solving we obtain x-y= 256...........(2) add 1 and 2 you will get 2x=1256 so x=628 put value of x in equation 1 so you would get _ 628+y=1000 y=372

Answer 2

[x+y]=1000
xsquare+ysquare=256000
=[x+y][x-y]=256000
=x-y=256
find the values