Question

The sum of the square of two numbers is 97 and the square of their difference is 25 the product of two numbers is

Answer 1

Answer:

solve this problem

I am sure you will get ans

Answer 2

Let the two numbers are x and y.

According to the question,

Sum of squares fo two numbers = 97

ie., x2+y2=97 ... (i)

and the square of their difference = 25

ie., (x−y)2=25 .. (ii)

=> x−y=5 .... (iii)

From eqn (ii)

(x2+y2)−2xy=25

=> 97 - 2xy = 25 (From eqn 1)

=> 2xy = 72

=< xy = 36 ... (iv)

Now, we have

(x+y)2=(x2+y2)+2xy

= 97 + 72 = 169

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