Question

# Two numbers are such that their sum multiplied by the sum of their squares is $$5500$$ and their difference multiplied by the difference of the squares is $$352$$. Then the numbers are ?

A
Prime numbers only
B
Odd positive integers
C
Prime but not odd
D
Odd but not prime

Solution

## The correct option is C Odd positive integersLet x and y = the numbers (x+y)(x2+y2)=5500(x+y)(x2+y2)=5500   ←   Equation (1)(x−y)(x2−y2)=352(x−y)(x2−y2)=352   ←   Equation (2) (x+y)(x2+y2)(x−y)(x2−y2)=5500352(x+y)(x2+y2)(x−y)(x2−y2)=5500352(x+y)(x2+y2)(x−y)(x−y)(x+y)=1258(x+y)(x2+y2)(x−y)(x−y)(x+y)=1258x2+y2(x−y)2=1258x2+y2(x−y)2=12588x2+8y2=125(x2−2xy+y2)8x2+8y2=125(x2−2xy+y2)117x2−150xy+117y2=0117x2−150xy+117y2=0(13x−9y)(9x−13y)=0(13x−9y)(9x−13y)=0 For 13x - 9y = 0y=139xy=139x   ←   Equation (3) From Equation (2)(x−139x)[x2−(139x)2]=352(x−139x)[x2−(139x)2]=352(−49x)(−8881x2)=352(−49x)(−8881x2)=352(−49x)(−8881x2)=352(−49x)(−8881x2)=352352729x3=352352729x3=352x3=729x3=729x=9x=9       answer From Equation (3)y=139(9)y=139(9)y=13y=13Mathematics

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