Question

If (x-1/x)=9 then x⁴+1/x⁴ find the value

Answer 1

Step-by-step explanation:

Given:

x-1/x=9

taking 4 as power on both sides

so, (x-1)^4/x^4 =9^4

x^4 + 1/ x^4 = 6561

so, answer is 6561.

Answer 2

6887

Step-by-step explanation:

$x-\frac{1}{x}=9-(i)\\x^4+\frac{1}{x^4}=?\\x-\frac{1}{x}=9$

Squaring both sides in equation (i)

$(x-\frac{1}{x})^2=(9)^2\\x^2+(\frac{1}{x})^2-2\times x\times\frac{1}{x}=81\\x^2+\frac{1}{x^2}=81+2\\x^2+\frac{1}{x^2}=83-(ii)$

again squaring both side in equation (ii)

$(x^2+\frac{1}{x^2})^2=(83)^2\\(x^2)^2+(\frac{1}{x^2})+2\times x^2+\frac{1}{x^2}=6889\\x^4+\frac{1}{x^4}+2=6889\\x^4+\frac{1}{x^4}=6889-2\\x^4+\frac{1}{x^4}=6887$