Class 11 Mathematics Q2 (Quadratic equation)

Q.1 Find two numbers such that each one is the square of the other.

Step 1:

Let the two numbers be $x$ and $y$.

According to question.

• $x$ is the square of $y$ → $x=y^2$
• $y$ is the square of $x$ → $y=x^2$

So,

$$x=y^2\text{and}y=x^2$$

Step 2:

From the second equation: $y=x^2$.

Put this into the first equation:

$$x=(x^2{)}^2$$

Step 3: Simplify

$$x=x^4$$

Step 4:

$$x^4-x=0$$

Factorize:

$$x(x^3-1)=0$$

Step 5:

• Case 1: $x=0$ Then $y=x^2=0^2=0$. So one solution is $(0,0)$.
• Case 2: $x^3-1=0⟹x^3=1$. The real solution is $x=1$. Then $y=x^2=1^2=1$. So another solution is $(1,1)$.

Answer: 0 and 1