Question

sum of two numbers is 20 and difference between their sqares is 100.find the product

Answer 1

$\textbf {Hey there, here is the solution.}$

.............................................................................................

STEP 1: Define x:

Let one number be x

The other number is 20 - x

.............................................................................................

STEP 2: Form the equation:

The difference between their square is 100

⇒ x² - (20 - x)² = 100

.............................................................................................

STEP 3: Solve x:

x² - (20 - x)² = 100

x² - (20² - 40x + x²) = 100

x² - 400 + 40x - x² = 100

40x - 400 = 100

40x = 500

x = 12.5

.............................................................................................

STEP 4 Find the numbers:

One number = x = 12.5

The other number = 20 - x = 20 - 12.5 = 8.5

............................................................................................. .

Answer: The numbers are 12.5 and 8.5

.............................................................................................

⭐$\textbf {Cheers}$⭐