Question
1)Find the exact solutions of the system of equations x^2 + 2y^2 = 18 and x = 2y.
x=2y
x^2+2y^2=18
(2y)^2+2y^2=18
4y^2+2y^2=18
6y^2=18
y^2=3
y=+-ã3
x=2(+-ã3)
x=+-2ã3
(+-2sqrt3,+-sqrt3)
2)Simplify, (d/(d^2-9)) + (5/(2d+6))
[d / (d^2 - 9)] + [5 / (2d + 6)]
= [d / (d - 3) (d +3)] + [5 / 2 (d + 3)]
= [2d + (5 {d - 3})] / [2 (d + 3) (d - 3)]
= [2d + 5d - 15] / [2 (d + 3) (d - 3)]
= (7d - 15) / [2 (d + 3) (d - 3)]
= (7d - 15) / (2d^2 - 18)
x=2y
x^2+2y^2=18
(2y)^2+2y^2=18
4y^2+2y^2=18
6y^2=18
y^2=3
y=+-ã3
x=2(+-ã3)
x=+-2ã3
(+-2sqrt3,+-sqrt3)
2)Simplify, (d/(d^2-9)) + (5/(2d+6))
[d / (d^2 - 9)] + [5 / (2d + 6)]
= [d / (d - 3) (d +3)] + [5 / 2 (d + 3)]
= [2d + (5 {d - 3})] / [2 (d + 3) (d - 3)]
= [2d + 5d - 15] / [2 (d + 3) (d - 3)]
= (7d - 15) / [2 (d + 3) (d - 3)]
= (7d - 15) / (2d^2 - 18)