Question

Which of the one is correct . Kindly tell the correct answer .

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Answer 1

Question

Given that

$\mathbb{D}=\{t|t^3=t,\ t\in\mathbb{R}\}$,

which is correct between

$\mathbb{D}=\{-1,0,1\}$ or $\mathbb{D}=\{-1,1\}$?

________________________________________

Solution

Given, $\mathbb{D}=\{t|t^3=t,\ t\in \mathbb{R}\}$.

The elements of the set $\mathbb{D}$ satisfy $t^3=t$. Then, we have to solve this equation and find its roots. Let's begin with how we can solve this equation.

The method of solving an equation is vanishing R.H.S and make it 0. Then we can solve the equation if we know when the L.H.S and the R.H.S equal.

This requires factorization. Let's begin.

Given, $t^3=t$

$\rightarrow t^3-t=0$

$\rightarrow t(t^2-1)=0$

$\rightarrow (t-1)t(t+1)=0$

So we know when two sides equal to zero. It is when each factor becomes zero.

• $t-1=0\rightarrow t=1$
• $t=0$
• $t+1=0\rightarrow t=-1$

So, $t=-1,0,1$ satisfy the equation. And, the answer must be $\mathbb{D}=\{-1,0,1\}$.

This is the required answer.

Answer 2

Answer:

Question

Given that

$\mathbb{D}=\{t|t^3=t,\ t\in\mathbb{R}\}$,

which is correct between

$\mathbb{D}=\{-1,0,1\}$ or $\mathbb{D}=\{-1,1\}$?

________________________________________

Solution

Given, $\mathbb{D}=\{t|t^3=t,\ t\in \mathbb{R}\}$.

The elements of the set $\mathbb{D}$ satisfy $t^3=t$. Then, we have to solve this equation and find its roots. Let's begin with how we can solve this equation.

The method of solving an equation is vanishing R.H.S and make it 0. Then we can solve the equation if we know when the L.H.S and the R.H.S equal.

This requires factorization. Let's begin.

Given, $t^3=t$

$\rightarrow t^3-t=0$

$\rightarrow t(t^2-1)=0$

$\rightarrow (t-1)t(t+1)=0$

So we know when two sides equal to zero. It is when each factor becomes zero.

$t-1=0\rightarrow t=1$

$t=0$

$t+1=0\rightarrow t=-1$

So, $t=-1,0,1$ satisfy the equation. And, the answer must be $\mathbb{D}=\{-1,0,1\}$.

This is the required answer.