Question

x² + 1/x²= 82/9 by quadratic formula
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Answer 1

Step-by-step explanation:

Given : x^2 + 1/x^2=82/9

=>x^4+1=82x^2/9

=>9x^4 + 9=82 x^2

=> 9x^4 - 82x^2 + 9=0

now,

let x^4= y^2 x^2= y

so ,we have qua. equ. now is...

9y^2 - 82y + 9 = 0

using quadratic formula,

y = -b +_ √b^2-4ac

2a

= -(-82) +-√(-82)^2 -4×9×9

2×9

=82+-√6724 - 324

18

=82+- √6400

18

= 82 +- 80

18

now, on taking sign (+)

y=82 + 80

18

y= 9

Then ,

y= 9

x^2=9

x=√9

x=3

taking sign(-)

y=82-80

18

y=2/18

y= 1

9

Then ,

y=1/9

x^2=1/9

x= √1/9

x= 1/3

so the value of x by using qua. formula are.......

x=3, x= 1/3

i hope this will help you

( if you are in class 10th, then this chapter is important for you.)