The sum of the squares of two numbers is 3341 and the diference of their squares

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Question
The sum of the squares of two numbers is 3341 and the diference of their squares is 891. The numbers are :
Options
A. 35 and 46
B. 35 and 50
C. 40 and 55
D. 45 and 60

Correct Answer

35 and 46

Explanation

Let the numbers be x and y. Then,

x^2+y^2=3341......(1)

x^2-y^2=891......(2)

Adding (i) and (ii), we get : 2x^2=4232 or x^2= 2116 or x =46

Subtracting (ii) from (i), we get : 2y^2= 2450 or y^2 = 1225 or y = 35

So, the numbers are 35 and 46

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