Question

If x+1/x=9 and x-1/x=6, find the value of x⁴-1/x⁴.​

Answer 1

Answer:

4266

Step-by-step explanation:

given x + 1/x  = 9  &  x - 1/x  = 6

take x + 1/x  = 9

=> (x+1/x)² = 9²

=>  $(x^2+\frac{1}{x^2})$ + 2 = 81

=> $(x^2+\frac{1}{x^2})$ = 81-2 = 79

we know,  $x^4$-$\frac{1}{x^4}$ = $(x^2+\frac{1}{x^2})$$(x^2-\frac{1}{x^2})$

=>  $x^4$-$\frac{1}{x^4}$ = $(x^2+\frac{1}{x^2})$$(x+\frac{1}{x})(x-\frac{1}{x})$

              = 79*9*6

              = 711*6

              = 4266