UGC NET Computer Science December 2019 | Question 18

Question 18

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The sum of a number and its inverse is -4. The sum of their cubes is:

1. 1. -52
2. 2. 52
3. 3. 64
4. 4. -64

Explanation:

let x is a given number and consider that y is the inverse of x.

It is given that
x + y = - 4
∴ y = -4 - x
As, y is inverse of x
∴  x*y = xy = 1

Now sum of their cube
= x³ + y³
by using formula: x³+y³=(x+y)³-3xy(x+y)
= (x+y)³ - 3xy(x+y)

Now, replace (x+y) by -4
= (-4)³ - 3xy (-4)
= -64 +12xy

Now, replace xy by 1
= -64+12
= -52

So, Option 1 is the right answer

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