Question

The sum of a number and its square is 63/4. Find the numbers.

Answer 1

Let the number be x.

Given that the sum of x and its square = 63/4

⇒ x + 𝑥² = 63/4

⇒ 4x + 4x² - 63 = 0

⇒ 4x² + 4x - 63 = 0

⇒ 4x² + 4x - 63 = 0 ....................(i)

The value of x can be found by the formula

`x=(-b+-sqrt(b^2-4ac))/(2a)`

⇒ here a = 4, b = 4 and c = -63 from (i)

`x=(-4+-sqrt(16-4xx4xx-63))/(2xx4)`

`=(-4+-sqrt(16+16xx63))/(2xx4)`

`x=(-4+-sqrt(16+1008))/8`

Therefore,

`x=(-4+sqrt(16+1008))/8=7/2`

Or

`x=(-4-sqrt(16+1008))/8=-9/2`

∴ The values of x i. e. , the numbers is 7/2 , -9/2.
.