Answer:
y = ± √ 7/2
Explanation:
2*y^2-8-(6-2*y^2)=0
(2 • (y2)) - 8) - (6 - 2y2) = 0
(2y2 - 8) - (6 - 2y2) = 0
Pull out like factors :
4y2 - 14 = 2 • (2y2 - 7)
4.2 Factoring: 2y2 - 7
difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
2 • (2y2 - 7) = 0
5.1 Solve : 2 = 0
5.2 Solve : 2y2-7 = 0
Add 7 to both sides of the equation :
2y2 = 7
Divide both sides of the equation by 2:
y2 = 7/2 = 3.500
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
y = ± √ 7/2