Question

If x2 + y2 = 65 and xy = 8, find (x – y)2

Answer 1

Answer:

$\rm 49$

Step-by-step explanation:

We have,

$\rm x^2+y^2=65$

$\rm xy=8$

$\rm 2xy=16$

$\rm (x-y)^2 = x^2+y^2-2xy$

$\rm\Rightarrow 65-2(8)$

$\rm\Rightarrow 65-16$

$\rm\Rightarrow 49$

Answer 2

Answer:

49

Step-by-step explanation:

x^2+y^2=65

add 2xy and subtract 2xy left hand side.

x^2+y^2-2xy+2xy=65

(x^2+y^2-2xy)+2xy=65

underlined expression can be written as( x-y) ^2

(x-y) ^2+2xy=65

put value of xy and transfer it to right side

(x-y) ^2=65-2xy

(x-y) ^2=65-2*8

(x-y) ^2=65-16

(x-y) ^2=49