Question

using the concept of quadratic equations, solve the question below.
Two positive numbers differ by 5 and the sum of their squares is 193. Find the two numbers.

Answer 1

Answer:

x - y = 5

x² + y² = 193

x² + (x - 5)² = 193

x² + x² - 10x + 25 = 193

2x² - 10x - 168 = 0

x² - 5x - 84 = 0

(x + 7)(x - 12) = 0

x = 12 (x = -7 is not accepted)

The two numbers are 7 and 12.

Answer 2

Answer:

7 and 12.

Step-by-step explanation:

Let the 2 numbers be A and B Then:

A - B = 5 and

A^2 + B^2 = 193

--> (A - B)^2 + 2AB = 193

--> 5^2 + 2AB = 193

--> 2AB = 193 - 25 = 168

--> AB = 84

--> A = 84/B

Substituting in the first equation:

84/B - B = 5

84 - B^2 = 5B

B^2 + 5B - 84 = 0

(B + 12)(B - 7)

B = 7