The sum of a number and its square is \(\frac{63}{4}\), Find the numbe

1.	The sum of a number and its square is \(\frac{63}{4}\), Find the numbers.
Answer» Let the number be x. So, its square will be x². From the question, it’s given that sum of the number and its square is \(\frac{63}{4}\) Which means, x + x² = \(\frac{63}{4}\) ⇒ 4x + 4x² = 63 ⇒ 4x² + 4x – 63 = 0 Solving for x by factorization method, we have ⇒ 4x² + 18x – 14x – 63 = 0 ⇒ 2x(2x + 9) – 7(2x – 9) = 0 ⇒ (2x – 7)(2x + 9) = 0 Now, either 2x -7 = 0 ⇒ x = \(\frac{7}{2}\) Or, 2x + 9 = 0 ⇒ x = \(\frac{-9}{2}\) Thus, the numbers are \(\frac{7}{2}\) and \(\frac{-9}{2}\).

The sum of a number and its square is \(\frac{63}{4}\), Find the numbers.

Answer»

Let the number be x.

So, its square will be x².

From the question, it’s given that sum of the number and its square is \(\frac{63}{4}\)

Which means,

x + x² = \(\frac{63}{4}\)

⇒ 4x + 4x² = 63

⇒ 4x² + 4x – 63 = 0

Solving for x by factorization method, we have

⇒ 4x² + 18x – 14x – 63 = 0

⇒ 2x(2x + 9) – 7(2x – 9) = 0

⇒ (2x – 7)(2x + 9) = 0

Now, either 2x -7 = 0 ⇒ x = \(\frac{7}{2}\)

Or, 2x + 9 = 0 ⇒ x = \(\frac{-9}{2}\)

Thus, the numbers are \(\frac{7}{2}\) and \(\frac{-9}{2}\).