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The sum of two positive numbers is 5 and the sum of their cubes is 35. What is the sum of their squares?

Sagot :

x + y = 5    ⇒     y = 5 - x

Representation:
x = first number
5 - x = second number

Sum of their squares:
(x)³ + (5 - x)³ = 35
x³ + 125 - 75x + 15x² - x³ = 35
x³ - x³ + 15x² - 75x + 125 = 35
15x² - 75x + 125 - 35 = 0
15x² -  75x + 90 = 0

Factor out the GCF of the three terms: 15

Factor x² - 5x + 6


x - 2 = 0
x = 2

x - 3 = 0
x = 3

The two positive numbers are 2 and 3.

The sum of their squares = (2)² + (3)²
Sum of their squares = 4 + 9
Sum of their squares = 13

The sum of the squares of positive numbers 2 and 3 is 13.

To check:
Sum of the two positive numbers is 5.
2 + 3 = 5

Sum of their cubes is 35.
(2)³ + (3)³ = 35
(2)(2)(2) + (3)(3)(3) = 35
8 + 27 = 35
35 = 35





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