Answered

Makahanap ng mga solusyon sa iyong mga problema gamit ang IDNStudy.com. Sumali sa aming platform ng tanong at sagot upang makatanggap ng mabilis at eksaktong tugon mula sa mga propesyonal sa iba't ibang larangan.

the difference between two positive numbers is 7 and the square of their sum is 289. find the two numbers

Sagot :

Peachocoidn
a-b=7
a+b=c
c^2=289
c=17
12-5=7
12+5=17
17^2=289
so the two numbers are 12 and 5
The problem is involves quadratic equation.

x =  larger positive integer
y = smaller positive integer

x - y = 7        (the difference between two positive numbers)
- y =  7 - x
y = x - 7
y = x - 7 (smaller positive number in terms of x)

[x + (x-7)]² = 289     (the square of the sum of the two numbers)

(2x - 7)² = 289

 4x² - 14x - 14x + 49 = 289

4x² -28x + 49 - 289 = 0

4x² - 28x - 240 = 0

4 (x² - 7x - 60) = 0

Factor x² -7x - 60:
(x - 12) (x + 5) = 0

x - 12 = 0
x = 12

x + 5 = 0
x = -5

Choose the positive value, x = 12.

Substitute 12 to x:
Larger number: x = 12
Smaller number : x-7 = 12 - 7 = 5

ANSWER: The numbers are 12 and 5.

Check:
The difference of two positive numbers is 7.
12 - 5 = 7
7 = 7  (true)

The square of their sum is 289.
(12 + 5)² = 289
(17)² = 289
289 = 289  (true)