if a^2-4a-1=0 the find the value of a^4+ 1/a^a^4.
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Answered by
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a²-4a-1=0
a²-4a=1
a(a-4)=1
a-4=1/a
a-1/a=4.....(1)
Squaring on both sides
(a-1/a)²=4²
a²+1/a²-2=16
a²+1/a²=18
Squaring on both sides
(a²+1/a²)²=18²
a⁴+1/a⁴+2=324
a⁴+1/a⁴=322
Answered by
0
a² - 4 a - 1 = 0
==> a² - 4 a = 1
==> a ( a - 4 ) = 1
==> a - 4 = 1 / a
==> a - 1/a = 4
Squaring both sides we get :
==> ( a - 1/a )² = 4²
==> a² + 1/a² - 2×a×1/a = 16
==> a² + 1/a² - 2 = 16
==> a² + 1/a² = 16+2
==> a² + 1/a² = 18
Squaring both sides we get :
==> ( a² + 1/a² )² = 18²
==> a⁴ + 1/a⁴ + 2.a . 1/a = 324
==> a⁴ + 1/a⁴ + 2 = 324
==> a⁴ + 1/a⁴ = 324 - 2 ==> 322
The value is 322.
Hope it helps :-)
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