Question

Solve for x. X^2 + 1/x^2 = 82/9

Answer 1

Answer:

3 or 1/3 both of them can be negative also.this is because square of a negative number is positive

Step-by-step explanation:

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

(x+1/x)^2=x^2 +1/x^2+2

we know that x^2 +1/x^2=82/9

(x+1/x)^2=82/9+2or 100/9

x+1/x=(100/9)^1/2

x+1/x=10/3

(x^2 +1)/x=10/3

x^2 +1=10/3x

x^2-10/3x+1=0

factories

x^2 -3x-x/3+1

x(x-3) -1/3(x-3)

(x-1/3)and(x-3)are factors

x-1/3=0

x-3=0

x=3

x=1/3