Oxford Entrance Exam Problem 1

Algebra Level 2

The inequality $x^4<8x^2+9$ is satisfied precisely when

-3<x<-1

1<x<3

0<x<4

-1<x<9

-3<x<3

1 solution

Raj Magesh
May 30, 2015

Factorise the given expression to obtain:

$(x+3)(x-3)(x^2+1) < 0$

(EDIT: $x^2+1$ is always positive for $x \in R$ and so we don't need to consider its sign. Think of it as dividing both sides by $x^2+1$ , a positive number, so the inequality does not change.)

Draw a wavy curve, which shows the intervals where the above expression is positive and negative:

This gives us a solution set of $(-3,3)$ .

Moderator note:

It would be better to explain why $x^2 + 1 > 0$ in your solution rather than in your comment. Good standard approach nonetheless.

What about x^2 +1

Abhishek Chopra - 6 years ago

$x^2+1$ is always positive for $x \in R$ and so we don't need to consider its sign. Think of it as dividing both sides by $x^2+1$ , a positive number, so the inequality does not change.

Raj Magesh - 6 years ago

Thanks I didn't knew.

Abhishek Chopra - 6 years ago

Oxford Entrance Exam Problem 1

1 solution

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