The sum of the square of a positive number and the square of

The sum of the square of a positive number and the square of 4 more than the number is 80. What is the number? The positive number is The positive number is

Solution

FIRST PART: Let the positive number be n, then

n² + (n + 4)² = 80, or, 2 n² + 8 n + 16 = 80, or, n² + 4 n - 32 = 0

or, n² + 8 n - 4 n - 32 = 0, or, (n + 8) (n - 4) = 0

Hence, n = 4, Since, (n + 8) can\'t be zero as n > 0.

SECOND PART: The given relation for the height attained by the rocket is:

h = - 4.9 t² + 14.0 t + 2.1

When it will strike the ground, its height will be zero. Therefore

0 = -4.9 t² + 14.0 t + 2.1, or, 7 t² - 20 t - 3 = 0

or, 7 t² - 21 t + t - 3 = 0, or, (7 t + 1) (t - 3) = 0

This implies t = 3, since (7 t + 1) is not equal to zero as t > 0.

Hence t = 3 seconds