Question

sum of two numbers is 1000. and the difference between there squares is 25600
find the numbers

Answer 1

Given,

$= > sum \: of \: two \: number \: is \: 1000$

$= > the \: difference \: between \: there \: square \: is \: 25600$

To find :-

$the \: number$

Solution:-

Consider x and y to be the two numbers such that x is greater than or equal to y.

Therefore,

$x + y = 1000$

Since, the difference between the squares of the two numbers is 256000.

Therefore,

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

Thus, the system of equations that we have is

$x + y = 1000...........(i)$

$x - y = 256...............(ii)$

We add both the equations,

$(x + y) + (x - y) = 1000 + 256 \\ = > x + y + x - y = 1256 \\ = > 2x = 1256 \\ = > x = \frac{1256}{2} \\ = > x = 628$

By substituting the value of x in equation (i), we get,

$628 + y = 1000 \\ = > y = 1000 - 628 \\ = > y = 372$

Therefore, the two numbers are 628 and 372.

Answer 2

Answer:

Hope this help...............