Question

If x+y=10,xy =2then find the value of (x-y)^2

Answer 1

Answer:

Given that,

x+y = 10

and

xy = 2.

Now we have to calculate value of

${(x - y)}^{2}$

We cannot calculate the value of above directly so we have to use the above given values as:-

${(x - y)}^{2} can \: be \: \\ written \: as \\ {(x + y)}^{2} - 4xy$

Now putting above values

${(x + y)}^{2} - 4xy \\ = {10}^{2} - 4(2) \\ = 100 - 8 \\ = 92$

So, value of required expression will be

$\bold{\green{\boxed{\boxed{ {(x - y)}^{2} = 92}}}}$

Answer 2

Answer:

92

Step-by-step explanation:

So, we know that,

= $(x+y)^{2} = x^{2} +y^{2} + 2xy$

= $(10)^{2} = x^{2} +y^{2} + 2(2)$

= $100 = x^{2} +y^{2} + 4$

= $100 -4 = x^{2} +y^{2}$

= $96 = x^{2} +y^{2}$

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

                      $= (x^{2} +y^{2}) - 2(2)$

                      $= (96) - 2(2)$

                      $= 96 - 4$

                      = 92