If x + y = 7 and xy = 4, then find the value of x^2 + y^2.

X+y=7

xy=4

in xy=4, divide both sides by any variable (lets say i divide it y y)

xy=4

x=4/y

Now substitute it to the 1st equation

x+y=7

4/y+y=7

Multiply both sides by y

4+y^2=7y

Change to standard form

y^2-7y=4

Use the square of something ...

y^2-7y+49/4=4+49/4

(y+7/2) ^2=65/4

Squareroot both sides

y+7/2=posinega (sqrt of 65) / 2

y = (sqrt of 65) / 2-7/2

or y = - (sqrt of 65) / 2-7/2