A) 45 |
B) 36 |
C) 54 |
D) 63 |
B) 36 |
Let the two numbers are x and y.
According to the question,
Sum of squares fo two numbers = 97
ie., \( \Large x^{2} + y^{2} = 97 \) ... (i)
and the square of their difference = 25
ie., \( \Large \left(x - y\right)^{2} = 25 \) .. (ii)
=> \( \Large x - y = 5 \) .... (iii)
From eqn (ii)
\( \Large \left(x^{2} + y^{2}\right)-2xy = 25 \)
=> 97 - 2xy = 25 (From eqn 1)
=> 2xy = 72
=< xy = 36 ... (iv)
Now, we have
\( \Large \left(x + y\right)^{2}= \left(x^{2} + y^{2} \right) + 2xy \)
= 97 + 72 = 169
\( \Large x + y =13 \) ... (V)
Now, from eqns (III) and (V) , we get
2x = 18
x = 9 and y = 4
The product of both the numbers = xy = 9 X 4 = 36