Question

If x= 14√2 find the value of (x-1/x)³​

Answer 1

\begin{gathered}x { }^{2} + 11x { }^{2} = 14 \ \\ (x + 1x {}^{2} ) - 2.x.1 x14 \\ take square root sides \\(x + 1x ) = 4 \\ then \\ x {}^{3} + 1x {}^{3} - 3.x.1x(x + 1x) \\ (x + 1x) {}^{3} - 3(x + 1x) \\ (4) {}^{3} - 3(4) \\ 64 - 12 \\ \\ 52 \: answer\end{gathered}

x

2

+11x

2

=14

(x+1x

2

)−2.x.1x14

takesquarerootsides

(x+1x)=4

then

x

3

+1x

3

−3.x.1x(x+1x)

(x+1x)

3

−3(x+1x)

(4)

3

−3(4)

64−12

52answer