Question

X-Y=8 & X^2 -Y^2=16m then find the product of X and Y

Answer 1

Given, x^2 - y^2 = 16

We know, a^2 - b^2 = ( a + b )( a - b ).

∴ x^2 - y^2 = ( x + y )( x - y )

⇒ ( x + y )( x - y ) = 16

From the question, value of ( x - y ) = 8

∴ ( x + y )( x - y ) = ( x + y )8

⇒ 8( x + y ) = 16

⇒ x + y = $\dfrac{16}{8}$

⇒ x + y = 2

Now, x - y = 8 and x + y = 2

Adding x - y and x + y

x - y = 8

x + y = 2

______

2x = 10

_____

x = $\dfrac{10}{2}$

x = 5

Substituting the value of x in x - y = 8

⇒ 5 - y = 8

⇒ 5 - 8 = y

⇒ - 3 = y

∴ x = 5 & y = - 3

∴ Product of x and y = 5 x ( - 3 )

                                  = - 15

Hence product of x and y is 15 .

Answer 2

Hey !!

X - Y = 8 ----------(1)

And,

X² - Y² = 16 ---------(2)

From equation (1) , we get

X - Y = 8

X = ( 8 + Y ) ---------(3)

Putting the value of X in equation (2) , we get

X² - Y² = 16

( 8 + Y )² - Y² = 16

(8)² + (Y)² + 2 × 8 × Y - Y² = 16

64 + Y² + 16Y - Y² = 16

16Y = 16 - 64

16Y = -48

Y = -3

Putting the value of Y in equation (3) , we get

X = ( 8 + Y ) = ( 8 - 3 ) = 5

Therefore,

Product of X and Y = 5 × -3 = -15