Question

If x+1/x = 4 then find x^4+1/x^4

Answer 1

x+1/x=4
x+1=4x
4x=x+1
4x-x=1
3x=1
x=1/3
we have to find x^4+1/x^4
Let put the value of x
$(\frac{1}{3} )^{4} + (\frac{1}{ \frac{1}{3} } )^{4}$
$\frac{1}{81} + 81$
$\frac{1 + 81 \times 81}{81}$
$\frac{1 + 6561}{81}$
$\frac{6562}{81}$

Answer 2

Answer:

$\underline{\bigstar\:\textsf{According to the Question Now :}}\\\\\implies\tt x + \dfrac{1}{x} = 4 \\\\ \textsf{Squaring Both Sides :} \\\\\implies\tt\bigg(x + \dfrac{1}{x} \bigg)^{2} ={(4)}^{2}\\\\\implies\tt {x}^{2} +\dfrac{1}{{x}^{2}} + 2 \times x \times \dfrac{1}{x} = 16 \\\\\\\implies\tt {x}^{2} +\dfrac{1}{{x}^{2}} = 16 - 2 \\\\\\\implies\tt {x}^{2} +\dfrac{1}{{x}^{2}} =14\\\\ \textsf{Squaring Both Sides :} \\\\\implies\tt \bigg({x}^{2} +\dfrac{1}{{x}^{2}}\bigg) ={(14)}^{2}\\\\\\\implies\tt {x}^{4} +\dfrac{1}{{x}^{4}} + 2 \times{x}^{2} \times\dfrac{1}{{x}^{2}} = 196\\\\\\\implies\tt {x}^{4} +\dfrac{1}{{x}^{4}} = 196 - 2\\\\\\\implies\large\boxed{\tt{x}^{4} +\dfrac{1}{{x}^{4}} = 194}$