Question

if sum of two positive numbers is 8 and product of that two positive numbers is 15 find sum of their square and sum of their cube

Answer 1

Answer:

34 and 152

Step-by-step explanation:

one number is 3 and another is 5

then 3^2+5^2 = 34

3^3+5^3 = 152

Answer 2

Answer:

36 and 152

Step-by-step explanation:

Given:

• Sum of two positive numbers = 8
• Product of the numbers = 15

To Find:

• Sum of their square
• Sum of their cube

Solution:

Let the first positive number be x.

Second positive number = y

A/Q,

x + y = 8

y = 8 - x ....(i)

xy = 15 ....(ii)

Putting y = 8 - x in (ii),

x (8 - x) = 15

=> - x² + 8x = 15

=> x² - 8x + 15 = 0

=> x² - 3x - 5x + 15 = 0

=> x(x - 3) - 5(x - 3) = 0

=> (x - 3)(x - 5) = 0

=> x - 3 = 0

x = 3

By eq. (i),

y = 8 - x = 8 - 3 = 5

Hence, two numbers are 3 and 5.

☆ Sum of their square = 3² + 5² = 9 + 25 = 36

☆ Sum of their cube = 3³ + 5³ = 27 + 125 = 152