Question

if x + y = 6 and x - y = 4 then find the value of (I) x2,- y2 (ii) xy.

Answer 1

x+y=6. (1)
x-y=4 (2)
From equation first and second , we get ,
2x=10
x=5

#1.) x^2-y^2= (5)^2-(1)^2= 25-1=24
#2.)xy=1×5=5

Answer 2

Given:

x + y = 6 and x - y = 4

To find:

i. $x^{2} -y^{2}$

ii. xy

Solution:

The value of ($x^{2} -y^{2}$) is 24 and xy is 5.

We can find the values by following the given steps-

We know that the required values can be obtained by using algebraic identities.

We know that the product of x+y and x-y gives $x^{2} -y^{2}$.

Similarly, $(x-y)^{2}$= $x^{2} +y^{2} -2xy$.

Using these, we can obtain the required values.

i. $x^{2} -y^{2}$=(x+y)×(x-y)

It is given that (x + y) = 6 and (x - y)= 4.

Using the values, we get

$x^{2} -y^{2}$=6×4

=24

ii. Now, we will calculate the value of xy.

We know that x-y=4 and x+y=6.

On adding the two, we get

(x+y)+(x-y)=6+4

x+y+x-y=10

2x=10

x=5

So, 5+y=6.

y=1.

Now, xy=5×1

xy=5

Therefore, the value of ($x^{2} -y^{2}$ ) is 24 and xy is 5.