please help me with QR question

[Questions]

If

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[RSD2014]

If x=3 what value of y satisfies x^2 < y^2 + xy - 1.

For my answer I got -5<y and 2<y. But the solutions say y<-5, 2<y.

why y<-5????

9 < y^2 +3y - 1

y^2 + 3y -10

(y-2)(y+5) > 0

y - 2 > 0
y > 2

y+5 > 0
y>-5

 

[Streetwolf]

If x=3 what value of y satisfies x^2 < y^2 + xy - 1.

For my answer I got -5<y and 2<y. But the solutions say y<-5, 2<y.

why y<-5????

9 < y^2 + 3y - 1
0 < y^2 + 3y - 10
0 < (y-2)(y+5)

<-----(-5)------(2)------->

Test all 3 spots...

y < -5: Plug in -8 and you get (-10)(-3) = 30 which is > 0.
y > -5 and y < 2 (the middle zone): Plug in 0 and get (-2)(5) = -10 which is < 0.
y > 2: Plug in 12 and get (10)(17) = 170 which is > 0.

So the choices that work are the two ends: y < -5 and y > 2.