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the sum of a natural number and its square is 156.Find the number
Most Upvoted Answer
the sum of a natural number and its square is 156.Find the number
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
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
Community Answer
the sum of a natural number and its square is 156.Find the number
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.
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the sum of a natural number and its square is 156.Find the number for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about the sum of a natural number and its square is 156.Find the number covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for the sum of a natural number and its square is 156.Find the number .
the sum of a natural number and its square is 156.Find the number for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about the sum of a natural number and its square is 156.Find the number covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for the sum of a natural number and its square is 156.Find the number .
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