.If = (3 + √8) then find the value of
[tex] {x}^{2} + \frac{1}{ {x}^{2} } [/tex]
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.If = (3 + √8) then find the value of
[tex] {x}^{2} + \frac{1}{ {x}^{2} } [/tex]
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[tex] \boxed{AnswEr}[/tex]
[tex] \sf \ {x}^{2} + \frac{1}{ {x}^{2} } = 34[/tex]
★GivEn :-
★ To Find :-
[tex] \boxed{Solution}[/tex]
1st Step :
[tex] \sf \: x = (3 + \sqrt{8} ) \\ \sf \: or \: \: \: \: \: \frac{1}{x} = \frac{1}{(3 + \sqrt{8} )} \\ \sf \: or \: \: \: \frac{1}{x} = \frac{(3 - \sqrt{8} )}{(3 + \sqrt{8)}(3 - \sqrt{8} ) } \\ \sf \: or \: \: \frac{1}{x} = \frac{(3 - \sqrt{8} )}{(9 - 8)} = (3 - \sqrt{8)} [/tex]
2nd Step :
[tex] \sf \: x + \frac{1}{x} \\ \sf \: = (3 + \sqrt{8} ) + (3 - \sqrt{8} ) \\ \sf \: = 3 + \sqrt{8} + 3 - \sqrt{8} = 6[/tex]
3rd Step :
[tex] \sf \: {x}^{2} + \frac{1}{ {x}^{2} } \\ = \sf \: (x + \frac{1}{x} )^{2} - 2 \times x \times \frac{1}{x} \\ \sf \: = {6}^{2} - 2 = 36 - 2 = 34[/tex]
[tex] \sf \therefore \: The \: answer \: is \: 34[/tex]
Answer:
34
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