If 3 x+1 3 x =3, find: 9 x^2+1 9 x^2 - Vidyadip

Question

If $3 x+\frac{1}{3 x}=3$, find: $9 x^2+\frac{1}{9 x^2}$

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Answer

$ 3 x+\frac{1}{3 x}=3$
$ \Rightarrow\left(3 x+\frac{1}{3 x}\right)^2=(3)^2$
$ \Rightarrow(3 x)^2+\left(\frac{1}{3 x}\right)^2+2 \times 3 x \times \frac{1}{3 x}=9$
$ \Rightarrow 9 x^2+\frac{1}{9 x^2}+2=9$
$ \Rightarrow 9 x^2+\frac{1}{9 x^2}=9-2$
$ \Rightarrow 9 x^2+\frac{1}{9 x^2}=7$

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