the sum of a natural number and its square is 156.Find the number

Question

Answer

Let the number is=x
and it's square=x²
It is given the sum of number and it's square =156
so x+x²=156 or x²+x-156 =0
solving the
x² +x -156
x²+13x-12x-156
x(x+13) -12(x+13)
(x+13) (x-12)
x+13=0 or x-12=0
x=-13 or x=12
we know that negative value is not is not taking
So x=12 is your answer.
Proof
12+12²=156
12+144=156
156=156 hence proved

Answer

Problem:

The sum of a natural number and its square is 156. Find the number.

Solution:

Let's assume the natural number as 'x'. Then we have the following equation:

x + x² = 156

Now we need to solve this equation to find the value of x.

Method 1: Quadratic Formula

This equation is a quadratic equation. We can solve it using the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

Here, a = 1, b = 1, and c = -156

Substituting these values in the formula, we get:

x = (-1 ± sqrt(1² - 4(1)(-156))) / 2(1)

x = (-1 ± sqrt(625)) / 2

x = (-1 ± 25) / 2

Therefore, x = 12 or x = -13. But we know that x is a natural number, so x can only be 12.

Method 2: Factoring

We can also solve this equation by factoring:

x + x² = 156

x² + x - 156 = 0

(x + 13)(x - 12) = 0

Therefore, x = 12 or x = -13. But we know that x is a natural number, so x can only be 12.

Answer:

The natural number is 12.

Answer

-13  and 12<div><br /></div>

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