Question

x=9+4 root 5 find x2+1/x2​

Answer 1

$\huge\mathbb{\underline{\red{SOLUTION:-}}}$

we have to find the value of

$\sf\implies x{}^{2}+\frac{1}{x{}^{2}}$

$\huge\mathbb{\purple{GIVEN:-}}$

$\sf x= 9+4\sqrt{5}$

1st find the value of $\sf \frac{1}{x}$

$\sf\implies \frac{1}{9+4\sqrt{5}}\\ \\ \sf\implies \frac{1}{9+4\sqrt{5}}\times \frac{9-4\sqrt{5}}{9-4\sqrt{5}}\\ \\ \sf\implies \frac{9-4\sqrt{5}}{(9){}^{2}-(4\sqrt{5}){}^{2}}\\ \\ \sf\implies \frac{9-4\sqrt{5}}{81-80}\\ \\ \sf\implies \frac{9-4\sqrt{5}}{1}\\ \\ \sf\implies 9-4\sqrt{5}$

The value of $\sf\frac{1}{x}= 9-4\sqrt{5}$

Find The value of $\sf x+\frac{1}{x}$

$\sf\implies 9+4\sqrt{5}+9-4\sqrt{5}\\ \\ \sf\implies 9+9+4\sqrt{5}-4\sqrt{5}\\ \\ \sf\implies 18$

The value of $\sf x+\frac{1}{x}=18$

Have to find:-

$\sf\implies x{}^{2}+\frac{1}{x{}^{2}}$

$\sf\implies (x+\frac{1}{x}){}^{2}=x{}^{2}+\frac{1}{x{}^{2}}+2$

$\sf\implies x{}^{2}+\frac{1}{x{}^{2}}+2=18\\ \\ \sf\implies x{}^{2}+\frac{1}{x{}^{2}}=18-2\\ \\ \sf\implies x{}^{2}+\frac{1}{x{}^{2}}=16$

The value of :-

$\underline{\sf x+\frac{1}{x{}^{2}}=16}$

Answer 2

▀▄ [_Hɪ Mᴀᴛᴇ_]▄▀

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