Answer
$(-3/2, -1/2)$ U $(1/2, 3/2)$
Work Step by Step
$16x^4-40x^2+9\leq0$
$x^2=y$
$16x^4-40x^2+9\leq0$
$16y^2-40y+9\leq0$
$16y^2-36y-4y+9\leq 0$
$4y(4y-9)-(4y-9)\leq0$
$(4y-9)(4y-1)\leq 0$
$4y-9=0$
$4y=9$
$4y/4 = 9/4$
$y=9/4$
$4y-1=0$
$4y=1$
$4y/4=1/4$
$y=1/4$
$y=9/4$
$x^2=9/4$
$\sqrt {x^2} = \sqrt {9/4}$
$x=-3/2, 3/2$
$y=1/4$
$x^2=1/4$
$\sqrt {x^2} = \sqrt {1/4}$
$x=-1/2, 1/2$
(-infinity, $-3/2)$
$(-3/2, -1/2)$
$(-1/2, 1/2)$
$(1/2, 3/2)$
$(3/2$, infinity)
Let $x=-2$, $x=-1$, $x=0$, $x=1$, $x=2$
$x=-2$
$16x^4-40x^2+9\leq0$
$16(-2)^4-40(-2)^2+9\leq0$
$16*16-40*4+9\leq 0$
$256-160+9\leq 0$
$96+9\leq 0$
$105 \leq 0$ (false)
$x=-1$
$16x^4-40x^2+9\leq0$
$16(-1)^4-40(-1)^2+9\leq0$
$16*1-40+9\leq 0$
$16-31\leq 0$
$-15 \leq 0$ (true)
$x=0$
$16x^4-40x^2+9\leq0$
$16*0^4-40*0^2+9\leq0$
$16*0-40*0+9\leq 0$
$0-0+9\leq 0$
$9\leq 0$ (false)
$x=1$
$16x^4-40x^2+9\leq0$
$16(1)^4-40(1)^2+9\leq0$
$16-40+9\leq 0$
$16-31\leq 0$
$-15 \leq 0$ (true)
$x=2$
$16x^4-40x^2+9\leq0$
$16(2)^4-40(2)^2+9\leq0$
$16*16-40*4+9\leq 0$
$256-160+9\leq 0$
$96+9\leq 0$
$105 \leq 0$ (false)
