Question

Solve for x : x^2 + 1/x^2 = 82/9

Answer 1

Answer:

x has four solutions: 1/3, -1/3, 3 and -3

Step-by-step explanation:

Please see attached file.

Answer 2

Step-by-step explanation:

Let, x²=y

=> y+1/y=82/9

(y²+1)/y=82/9

y²+1=82y/9

multiply whole equation by 9

9y²+9=82y

9y²+9-82y=0

9y²-82y+9=0

Now solve this equation by middle term splitting method

9y²-81y-y+9=0

9y(y-9)-1(y-9)=0

(y-9)(9y-1)=0

y-9=0 and 9y-1=0

y=9 and y=1/9

Since,

Acc. to our assumption

x²=y

x²=9 and x²=1/9

x=√9 and x=√(1/9)

x=±3 and x=±(1/3)