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maths question

How to solve these questions

1. x^2 (10 - x^2)=9


2. 5/x^2 +4/x -1 =0
1. x2(10−x2)=9x^{2}(10-x^{2})=9 Firstly, expand then move everything to one side.

10x2−x4=910x^{2}-x^{4}=9

−x4+10x2−9=0-x^{4}+10x^{2}-9=0

−(x4−10x2+9)=0-(x^{4}-10x^{2}+9)=0 Multiply the whole equation by −1-1 to get rid of the minus outside of the bracket. You don't have to factorise out a factor of −1-1, I just did it to make it look easier to deal with.

x4−10x2+9=0x^{4}-10x^{2}+9=0

Just to make it simpler, let u=x2⇒u2−10u+9=0u=x^{2} \Rightarrow u^{2}-10u+9=0. One you've found your solutions of uu, substitute back in x2x^{2} and then solve for your values of xx

2. 5x2+4x−1=0\frac{5}{x^{2}}+\frac{4}{x}-1=0 Multiply the whole equation by x2x^{2} to get rid of the fractions.

Therefore, 5+4x−x2=05+4x-x^{2}=0.

You should be able to work from here.
(edited 6 years ago)

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