Question

If x-1/x=6 find the value of x square+1/x square and x power4 +1/x power4.

Answer 1

( x - 1 / x ) = 6

==> Squaring both sides we get :

==> ( x - 1 / x )² = 6²

==> x² + 1 / x² - 2.x.1/x = 36

==> x² + 1 / x² - 2 = 36

==> x² + 1 / x² = 36 + 2

==> x² + 1 / x² = 38

Again squaring both sides :

( x² + 1 / x² ) = 38

==> x⁴ + 1 / x⁴ + 2.x².1/x² = 1444

==> x⁴ + 1 / x⁴ + 2 = 1444

==> x⁴ + 1 / x⁴ = 1444 - 2

==> x⁴ + 1 / x⁴ = 1442

ANSWERS :

x² + 1 / x² = 38

x⁴ + 1 / x⁴ = 1442

Hope it helps :-)

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