Question

t-1/t=8 then find the value of t^3 + 1/t^3

Answer 1

Answer:

536

Step-by-step explanation:

t-1/t=8

squaring both sides

(t-1/t)²=8²

identity:(t-1/t)²=t²+1/t²-2

64= t²+1/t²-2

t²+1/t²=66

identity:t³-1/t³=(t-1/t)(t²+1/t²+1)

[as t×1/t=1]

[main identity=a³-b³=(a-b)(a²+b²+ab)]

substitute the values

t-1/t=8 t²+1/t²=66

t³-1/t³=8×(66+1)

t³-1/t³=67×8

=536

all in [ ] brackets is for reference

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