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