Question

the sum of two number is 1000 and the difference between their square is 256000 find the numbers.

Answer 1

Let one number be 'x' and another be 'y'
A/Q
$x + y = 1000....(i) \\ {x}^{2} - {y}^{2} = 256000....(ii) \\ = > x = 1000 - y...(iii) \\ by \: substituting \: value \: in \: (ii) \\ = > {(1000 - y)}^{2} - {y}^{2} = 256000 \\ = > 1000000 + {y}^{2} - 2000y + {y}^{2} = 256000 \\ = > - 2000y = - 744000 \\ = > y = \frac{744000}{2000} \\ = > y = 372 \\ by \: substituting \: value \: of \: y \: in \: (i) \\ x + 372 = 1000 \\ = > x = 628$

Answer 2

Hiii here is ur solution

Let the larger no. be x

and smaller no. be y

According to the question

x+ y = 1000.....(1)

xsq - ysq = 256000.....(2)

on dividing 2 by 1

xsq - ysq / x + y = 256000/ 1000

X-y= 256.....(3)

Adding 1 and 3

x + y = 1000 + x - y = 256

2x = 1256

x = 1256/2
x = 628


substitute x = 628 in 1

628 + y = 1000

y = 1000 - 628

y = 372

hence, the required no. are 628 and 372.
hope it helps you