Question

plz answer with explanation

Answer 1

Let x be 'a' and 1/x be 'b'
a-b = 5 ( given)...................……………...........(1)
Note that ab = 1
Squaring on both sides, we get,
a²+b²-2ab= 25
a²+b²-2 = 25
a²+b²= 27
So, a²+b²+1 = 27+1 = 28 ..............................(2)
a³-b³= (a-b)(a²+ab+b²)
Substituting the values which we got in (1) and (2) in this , we get ,
a³-b³= (5)(28)
=140

:. x³-1/x³ = 140

Hope this helps!!!
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Answer 2

Given x - 1/x = 5.

On cubing both sides, we get

(x - 1/x)^3 = (5)^3

x^3 - 1/x^3 - 3 * x * 1/x(x - 1/x) = 125

x^3 - 1/x^3 - 3(5) = 125

x^3 - 1/x^3 - 15 = 125

x^3 - 1/x^3 = 125 + 15

x^3 - 1/x^3 = 140.



Hope this helps!