Question

Rajiv has a number x in his mind. He finds out that the square of x is less than x. What is the range of x?
(a) x is more than 0
(b) x is less than 1
(c) x is more than 0, but less than 1
(d) This is not possible

Answer 1

(c) X is more than 0 but less than 1
cause
$x {2} < x \\ x {2} - x < 0 \\ x(x - 1) < 0 \\ x < 1(x = not \: 0)$

Answer 2

Answer:

Required range of x is $1 > x > 0$

Step-by-step explanation:

Given a number x and the number x is greater than square of x.

Therefore

$x > {x}^{2} \\ x - {x}^{2} > 0 \\ x(1 - x) > 0$

If product two number is greater than zero then they are separately greater than zero.

So,

$x > 0$

or,

$(1 - x) > 0 \\ 1 > x \\ x < 1$

Therefore we can say $1 > x > 0$

Hence x is less than one and greater than zero.

For example, if $x = \frac{1}{2}$ where $1 > \frac{1}{2} > 0$

then,

$\frac{1}{2} > (\frac{1}{2} )^{2} \\ \frac{1}{2} > \frac{1}{4}$

This is a problem of Algebra.

Some important Algebra formulas.

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

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2) https://brainly.in/question/1169549