Question

For what positive value of x is d smaller?

Answer 1

9/16 ≤ x(x + 1)(x + 2)(x + 3)
= [x(x + 3)][(x + 1)(x + 2)]
= [x^2 + 3x][x^2 + 3x + 2]
= [(x^2 + 3x + 1) - 1][(x^2 + 3x + 1) + 1]
= (x^2 + 3x + 1)^2 - 1^2

0 ≤ (x^2 + 3x + 1)^2 - 1^2 - 9/16
= (x^2 + 3x + 1)^2 - (16 + 9)/16
= (x^2 + 3x + 1)^2 - 25/16
= (x^2 + 3x + 1)^2 - (5/4)^2
= (x^2 + 3x + 1 - 5/4)(x^2 + 3x + 1 + 5/4)
= (x^2 + 3x - 1/4)(x^2 + 3x + 9/4)
= (x^2 + 3x - 1/4) * (x + 3/2)^2

we know (x + 3/2)^2 is always ≥ 0 for all x,
so we only need to solve for
x^2 + 3x - 1/4 ≥ 0
(x + 3/2)^2 ≥ 10/4
x + 1.5 ≤ -√2.5 or x + 1.5 ≥ √2.5

since x > 0,
x ≥ (√10 - 3)/2

answer, x = (√10 - 3)/2


i got it from yahoo answers. hope it helps! :)

Answer 2

y=x^2-9
For what positive value of x is d smaller?

Answer 3

sorry idk got the answer online.