If The sum of a Number and Its Square is 182, What is the Number?

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• Explanation

• Solution

Explanation

• If the sum of a number and its square is 182.

The number can be figure out in this way.

Let suppose the number is y.

Square of y

y²

Sum of y² and y equals 182

y² + y = 182 ________ (i)

Through equation (i) we can easily find out the value of y (y = 13).

To Find

Number = ?

Solution

Let suppose

Number = y

According to the given condition

y² + y = 182

y² + y – 182 = 0

y² + 14y – 13y – 182 = 0

y(y + 14) – 13(y + 14) = 0

(y + 14)(y – 13) = 0

y + 14 = 0           or                y – 13 = 0

y = -14 (not possible)           or                y = 13 (possible)

Required Number = 13 answer

Conclusion

If the sum of a number and its square is 182, the number is  13.