The sum of 2 non zero positive integers is 16. Positive difference of the squares of these 2 integer

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16 Mar 2011 x and y

The sum of 2 non zero positive integers is 16. Positive difference of the squares of these 2 integers is a perfect square non zero integer. Difference of these 2 non zero integers is

OPtion

1) 1
2) 2
3) 3
4) 4
5) 5
6) 6
7) 8
8) 9
9) 11
10) 12

Solution

These non zero integers are 6 and 10
and the third number is 64

Correct Option: 4 Best Solution (10)

A.P.Singh   13 years AGO

The sum of 2 non zero positive integers x and y is 16. Positive difference of the squares of these 2 integers ( x^2-y^2) is a perfect square non zero integer. Difference of these 2 non zero integers is such that (x-y)is also a perfect square. Poosible values are 4 and 9. In case of 9, values of x and y are not integers.

So x-y=4 is possible .

Like? Yes (4) | No (2)  

sanjeev   13 years AGO

no are 10 & 6
10+6=16
10^2-6^2
100-36
=64
which is perfect square of 8

Like? Yes (3) | No (2)  

Karthick Babu   13 years AGO

from the question,
x+y=16;x-y=option(any one);and x & y both non zero +ve int.So definitely the option will be even no.
So neglect odd number from option remaining only 5 option such as(opt:2,4,6,7,10)Solve that two equation for different even ans to get x & y.
So the ans is option4->4.

Like? Yes (4) | No (4)  

YadeeshKumar   13 years AGO

x+y=16
x^2-y^2=perfect square
x=10 and y=6
100-36=64 is a perfect square
so x-y=10-6=4(option 4)

Like? Yes (3) | No (3)  

Dundi   13 years AGO

10+6 = 16 and the difference of suares is 64 (also it is a perfect square)

Finally the diffrence between them is 4 (10-6)

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Suresh Varma P   13 years AGO

As per the condition:
X + Y = 16
X^2 - Y^2 = Z^2 (perfect square)
So (X + Y) * (X - Y) = Z^2
(X - Y) = Z^2 / (X + Y)
(X - Y) = Z^2/16

As the sum of X & Y is 16 the possible combination to get the perfect square is (10 - 6)=4 which makes Z a perfect square.

Ans: Option 4

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Balakumaran N.A   13 years AGO

x+y=16. We can conclude, 10+6=16 so that 100-36=64.
The difference is 4.

Like? Yes (2) | No (2)  

A J V   13 years AGO

x+y=16
x^2-y^2=perfect square
x=10 and y=6
100-36=64 is a perfect square
so x-y=10-6=4(option 4)

Like? Yes (2) | No (2)  

Murthy Ch.v.v.s.s.s.   13 years AGO

Given: x+y=16; and x^2-y^2 = Perfect square; X n Y are Non zero Integers;
so The possible values for X-Y can be 1,4 and 9.
Out of these, X and Y are Integers only in the case of X-Y =4.
So x-y=4 n option is 4

Like? Yes (1) | No (1)  

goutam Choudhury   13 years AGO

10^-6^2=8^2.10-6=4 option 4

Like? Yes (1) | No (2)