Name: Solving Free Fall Problem Using Quadratic Equation
Uploaded: 2019-07-19
Duration: 7 min 7 s
Description: In this video, we will learn how we can solve the problem of free fall effectively using the quadratic equation. Let's watch the video and learn.

Question

The difference of squares of two natural numbers is $45$ . The square of the smaller number is $8$ times the larger number. Find the two numbers.

Note: The question given in the textbook seems to be wrong. The correct question should be as below:

The difference of squares of two natural numbers is $45$ . The square of the smaller number is $4$ times the larger number. Find the two numbers.

Accepted Answer

Let the required smaller natural number be $x$ and larger natural number be $y$

It is given that the square of the smaller number is $4$ times the larger number.

$x^{2} = 4 y . . . . (1)$

According to the question,

$y^{2} - x^{2} = 45 . . . .$ $(2)$

Substituting value of $x^{2}$ from eq $(1)$ in eq $(2)$ , we get

$y^{2} - 4 y = 45$

So, the quadratic equation formed is, $y^{2} - 4 y - 45 = 0$

On splitting the middle term of $y^{2} - 4 y - 45 = 0$ , we get,

$\Rightarrow y^{2} - 9 y + 5 y - 45 = 0$

$\Rightarrow y (y - 9) + 5 (y - 9) = 0$

$\Rightarrow (y - 9) (y + 5) = 0$

$\Rightarrow (y - 9) = 0$ or $(y + 5) = 0$

$\Rightarrow y = 9$ or $y = - 5$

Since the natural numbers cannot be negative,

Thus, $y = 9$

So, $x^{2} = 4 (9) = 36$ $\Rightarrow x = 6$

Hence, the required natural numbers are $9$ and $6$

Important Questions on Quadratic Equations

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