Question

if the product of two consecutive natural number is 210 then determine the number.

please anyone solve this by Shri dhra charya formula.
otherwise I will report your answer.Note you will be mark as brain list if your answer is right.​

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

First natural number = x

Second consecutive natural number = x + 1

According to statement,

The product of two consecutive natural number is 210.

$\rm \: x(x + 1) = 210$

$\rm \: {x}^{2} + x = 210$

$\rm \: {x}^{2} + x - 210 = 0$

So, its a quadratic equation in x.

On comparing with ax² + bx + c = 0, we have

$\rm \: a = 1$

$\rm \: b = 1$

$\rm \: c = - 210$

We know, Shree dhar Acharya formula is given by

$\boxed{\sf{  \:\rm \: x \: = \: \frac{ - b \: \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} \: \: }}$

So, on substituting the values of a, b, c, we get

$\rm \: x \: = \: \frac{ - 1 \: \pm \: \sqrt{ {1}^{2} - 4(1)( - 210)} }{2(1)} \: \:$

$\rm \: x \: = \: \frac{ - 1 \: \pm \: \sqrt{ 1 + 840} }{2} \: \:$

$\rm \: x \: = \: \frac{ - 1 \: \pm \: \sqrt{841} }{2} \: \:$

$\rm \: x \: = \: \frac{ - 1 \: \pm \: 29 }{2} \: \:$

$\rm \: x \: = \: \frac{ - 1 \: + \: 29 }{2} \: or \: \frac{ - 1 \: - \: 29 }{2}$

$\rm \: x \: = \: \frac{ 28 }{2} \: or \: \frac{ - 30 }{2}$

$\rm\implies \:x = 14 \: \: or \: \: x \: = - 15 \{ \: rejected \: as \: - 15 \cancel\in N \}$

So, It means

First natural number is 14

Second natural number is 15

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Additional Information :-

Nature of roots :-

Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

Discriminant, D = b² - 4ac

Answer 2

QUESTION :

• if the product of two consecutive natural number is 210 then determine the number.

GIVEN :

• product of two consecutive natural number is 210

TO FIND :

• determine the number = ?

SOLUTION :

Let two consecutive natural numbers be

x and x + 1

According to question :

x × (x + 1) = 210

⇒x²+x - 210 = 0

Using middle tem splitting method, we get :

x² + 15x - 14 x - 210 = 0

x(x +15) - 14 (x +15) = 0

⇒ (x - 14) (x +15) = 0

⇒x=14, -15

x is a natural number thus can't be negative so,

x = 14

and x + 1 = 14 +1 = 15

Thus, the numbers are 14 and 15