Question

a number is 64 times the square of its reciprocal.the number is

Answer 1

let the no. be x

acc. to que.

x = 64*(1/X)²

X=64/x²

x*x²=64

x³=64

x=∛64

x=4

therefore the no. is 4

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Answer 2

The number is 4

Given :

A number is 64 times the square of its reciprocal

To find :

The number

Solution :

Step 1 of 2 :

Form the equation

Let the required number = n

By the given condition

$\displaystyle \sf{n = 64 \times \frac{1}{ {n}^{2} } }$

Step 2 of 2 :

Find the number

$\displaystyle \sf{n = 64 \times \frac{1}{ {n}^{2} } }$

$\displaystyle \sf{ \implies n \times {n}^{2} = 64}$

$\displaystyle \sf{ \implies {n}^{3} = 64}$

$\displaystyle \sf{ \implies {n}^{3} = {4}^{3} }$

$\displaystyle \sf{ \implies n = 4 }$

Hence the required number = 4

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