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Sum of two no is 1000 and difference between their Square is 256000 find the no |
| Answer» Let us suppose that the numbers are x and y.According to question it is given thatThe sum of the two numbers is 1000.Thus, we have x + y = 1000The difference between the squares of the two numbers is 256000.Therefore, we have x2 - y2 = 256000{tex} \\Rightarrow{/tex}\xa0(x + y)(x - y) = 256000{tex}\\Rightarrow{/tex}\xa01000(x - y) = 256000{tex}\\Rightarrow x - y = \\frac{{256000}}{{1000}}{/tex}{tex}\\Rightarrow{/tex}\xa0x - y = 256Therefore, we have two equationsx + y = 1000 ......(1)x - y = 256 .....(2)Here x and y are unknowns.We have to solve the above equations for x and y.Adding equation (1) and (2), we get(x + y) + (x - y) = 1000 + 256{tex}\\Rightarrow{/tex}\xa0x + y + x - y = 1256{tex}\\Rightarrow{/tex}\xa02x = 1256{tex}\\Rightarrow x = \\frac{{1256}}{2}{/tex}x = 628Substituting the value of x in the equation (1) we get,\xa0628 + y = 1000{tex}\\Rightarrow{/tex}\xa0y = 1000 - 628{tex}\\Rightarrow{/tex}\xa0y = 372Therefore the numbers are 628 and 372. | |