Question

If x - y = 6, xy = 8 find values of
x2+y2​

Answer 1

Answer:

x - y = 6, ==> x = 6 + y

x y = 8, ==> (6+y)y = 8,==> 6y + y 2 =8, ==> y 2 + 6y = 8

y 2 + 6y + 9 = 8 + 9, ==> y 2 + 6y + 9 = 17

y 2 + 6y + 9 = 17 , ==> (y + 3) 2 = 17, ==> y + 3 = ±17−−√ , ==>

y = ±17−−√ -3

xy = 8

x = 8y , ==> 8±17√−3 , ==> 3±17−−√

x 2 + y 2 = ?

(3−17−−√)2+(−3−17−−√)2=52

(3+17−−√)2+(−3+17−−√)2=52

Answer is: 52

Answer 2

Step-by-step explanation:

x=6+y

6+y *y = 8

6y+y^2=8

y^2=8-6y

(y+6)^2 +(8-6y)

y^2+36+12y +8-6y

44+6y+y^2

44+6y +8-6y

44+8

=52

therefore x^2+y^2 = 52