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Question

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

A
600,400
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B
628,372
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C
675,325
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D
728,262
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Solution

The correct option is B 628,372
Let the numbers are x and y
According to the question
x+y=1000.....eq1
x2y2=256000
x2y2=(x+y)(xy)
1000(xy)=256000
xy=256.....eq2
Adding eq1 and eq2
2x=1256x=628
Put the value of x in eq1
628+y=1000y=372
The numbers are 628 and 372

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