Quartic inequality by substitution
Quartic inequality by substitution
IP 3
9 marks
- Solve the inequality \(x^4-5x^2+4<0\).[4]
- Hence solve \((x+1)^4-5(x+1)^2+4<0\).[2]
- Show that \(x^4-5x^2+4\ge-\dfrac{9}{4}\) for all real values of \(x\), and find the values of \(x\) for which equality holds.[3]
Solution:
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Answer:(a) \(-2<x<-1\) or \(1<x<2\) (b) \(-3<x<-2\) or \(0<x<1\) (c) equality when \(x=\pm\dfrac{\sqrt{10}}{2}\)
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