Mister Exam

Other calculators

Solving inequalities/ 3/(x^2-30x+216)>=1(x^2-34x+288)

3/(x^2-30x+216)>=1(x^2-34x+288) inequation

A inequation with variable

The solution

You have entered [src] 
       3            2             
--------------- >= x  - 34*x + 288
 2                                
x  - 30*x + 216
$$\frac{3}{\left(x^{2} - 30 x\right) + 216} \geq \left(x^{2} - 34 x\right) + 288$$ 
3/(x^2 - 30*x + 216) >= x^2 - 34*x + 288
Solving inequality on a graph
Rapid solution [src] 
  /   /            / 4       3         2                     \         / 4       3         2                     \     \     /            / 4       3         2                     \        \     /       / 4       3         2                     \             \\
Or\And\x <= CRootOf\x  - 64*x  + 1524*x  - 15984*x + 62205, 2/, CRootOf\x  - 64*x  + 1524*x  - 15984*x + 62205, 1/ <= x/, And\x <= CRootOf\x  - 64*x  + 1524*x  - 15984*x + 62205, 3/, 18 < x/, And\CRootOf\x  - 64*x  + 1524*x  - 15984*x + 62205, 0/ <= x, x < 12//
$$\left(x \leq \operatorname{CRootOf} {\left(x^{4} - 64 x^{3} + 1524 x^{2} - 15984 x + 62205, 2\right)} \wedge \operatorname{CRootOf} {\left(x^{4} - 64 x^{3} + 1524 x^{2} - 15984 x + 62205, 1\right)} \leq x\right) \vee \left(x \leq \operatorname{CRootOf} {\left(x^{4} - 64 x^{3} + 1524 x^{2} - 15984 x + 62205, 3\right)} \wedge 18 < x\right) \vee \left(\operatorname{CRootOf} {\left(x^{4} - 64 x^{3} + 1524 x^{2} - 15984 x + 62205, 0\right)} \leq x \wedge x < 12\right)$$ 
((18 < x)∧(x <= CRootOf(x^4 - 64*x^3 + 1524*x^2 - 15984*x + 62205, 3)))∨((x < 12)∧(CRootOf(x^4 - 64*x^3 + 1524*x^2 - 15984*x + 62205, 0) <= x))∨((x <= CRootOf(x^4 - 64*x^3 + 1524*x^2 - 15984*x + 62205, 2))∧(CRootOf(x^4 - 64*x^3 + 1524*x^2 - 15984*x + 62205, 1) <= x))
Rapid solution 2 [src] 
        / 4       3         2                     \                / 4       3         2                     \         / 4       3         2                     \                / 4       3         2                     \ 
[CRootOf\x  - 64*x  + 1524*x  - 15984*x + 62205, 0/, 12) U [CRootOf\x  - 64*x  + 1524*x  - 15984*x + 62205, 1/, CRootOf\x  - 64*x  + 1524*x  - 15984*x + 62205, 2/] U (18, CRootOf\x  - 64*x  + 1524*x  - 15984*x + 62205, 3/]
$$x\ in\ \left[\operatorname{CRootOf} {\left(x^{4} - 64 x^{3} + 1524 x^{2} - 15984 x + 62205, 0\right)}, 12\right) \cup \left[\operatorname{CRootOf} {\left(x^{4} - 64 x^{3} + 1524 x^{2} - 15984 x + 62205, 1\right)}, \operatorname{CRootOf} {\left(x^{4} - 64 x^{3} + 1524 x^{2} - 15984 x + 62205, 2\right)}\right] \cup \left(18, \operatorname{CRootOf} {\left(x^{4} - 64 x^{3} + 1524 x^{2} - 15984 x + 62205, 3\right)}\right]$$ 
x in Union(Interval.Lopen(18, CRootOf(x^4 - 64*x^3 + 1524*x^2 - 15984*x + 62205, 3)), Interval.Ropen(CRootOf(x^4 - 64*x^3 + 1524*x^2 - 15984*x + 62205, 0), 12), Interval(CRootOf(x^4 - 64*x^3 + 1524*x^2 - 15984*x + 62205, 1), CRootOf(x^4 - 64*x^3 + 1524*x^2 - 15984*x + 62205, 2)))
    © Mister Exam – Calculator