Question

If x + y = 18 and x y = 72, what is the value of (x)2 +(y)2: find

Answer 1

Answer:

x2+y2=180

Step-by-step explanation:

x+y=18

x=18-y

Putting in xy=72

(18-y)y=72

18y-y2=72

Rearranging above quadratic equation

y2-18y+72=0

y2-12y-6y+72=0     (Splitting the middle term)

y(y-12)-6(y-12)=0

(y-12)(y-6)=0

y=12,6

If y=12

then x=18-12

x=6

If y=6

then x=18-6

x=12

Thus, for x=6, y=12

x2+y2=36+144 => 180

And for x=12, y=6

x2+y2=144+36 => 180