Question

$the \: sum \: of \: two \: number \: is \: 1000 \: and \: the \: difference \: their \: squares \: is \: 256000. \: find \: the \: numbers$
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Answer 1

$\huge \: answer \:$

Let the larger number be x and the smaller number be y.

then, x + y =1000

and

${x}^{2} + {y }^{2} = 256000$

on dividing (ii) by (i), we get:

$\frac{x {}^{2} - y {}^{2} }{x + y} = \frac{256000}{1000} = > x - y = 256$

we get:

$2x \: = 1256 => x = 628$

substituting x = 628 in (i), we get: y = 372

hence,the required number are 628 and 372.