Guys pleqse solve this question.
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Q. 47
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Guys pleqse solve this question.
It's urgent.
The best and the correct answer will be marked as Brainliest.
Q. 47
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Given : a^4 + (1/a^4) = 727.
It can be written as,
⇒ a^4 + (1/a^4) = 729 - 2
⇒ a^4 + (1/a^4) + 2 = 729
⇒ (a^2)^2 + (1/a^2)^2 + 2(a^2)(1/a^2) = 729
⇒ (a^2 + 1/a^2)^2 = 729
⇒ a^2 + 1/a^2 = 27.
Now, It can be written as
⇒ a^2 + (1/a^2) = 25 + 2
⇒ a^2 + (1/a^2) - 2 = 25
⇒ (a - 1/a)^2 = 25
⇒ a - 1/a = 5.
On cubing both sides, we get
⇒ (a - 1/a)^3 = (5)^3
⇒ a^3 - 1/a^3 - 3(a - 1/a)= 125
⇒ a^3 - 1/a^3 - 3(5) = 125
⇒ a^3 - 1/a^3 - 15 = 125
⇒ a^3 - 1/a^3 = 140.
Hope this helps!