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Question

The sum of two numbers is 1000 and the difference between their square is 256000. Find the numbers.
 



A
628, 372
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B
562, 438
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C
125, 875
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D
None of these
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Solution

The correct option is A 628, 372

Let the two numbers be x and y

x+y=1000   ....(1)

x2y2=256000

Using identity x2y2=(x+y)(xy)

(x+y)(xy)=256000.....(2)

xy=256 .....(3) [Substituting x+y=1000 ]

Adding (1) and (3) we get,

2x=1256x=628

Substituting x=628 in (1)

628+y=1000y=372


Mathematics

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