Delhi Police Constable Exam Model Paper 2

Question : 83 of 100

Marks: +1, -0

If sum of a number and its reciprocal is 4, then what is the sum of cube of that number and reciprocal of that cube?

Solution:

GIVEN:

X+1/X=4

FORMULA USED:

x^2 + 1/{x^2} =(x+1/x)^2 − 2

CALCULATION:
Let number = x

x+1/x=4

⇒

(x+1/x)^2=4^2=16

⇒

x^2+1/{x^2}+2=16

⇒

x^2+1/{x^2}=14

Now,

(x+1/x)(x^2+1/{x^2})=4×14

⇒

x^3 + 1/x+x+1/{x^3}=56

x^3 + 1/{x^3} + x + 1/x= 56

⇒

x^3 + 1/{x^3} + 4 = 56

⇒

x^3 + 1/{x^3} = 52

Smart TrickIf x + 1/x = a, then

x^3+ 1/x^3= a^3– 3a

Here, a = 4,
∴

x^3+ 1/x^3= 4^3- 3 × 4 = 64 – 12 = 52

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