Question

The sum of two numbers is 16. The substraction of their squies is 32 . The Two numbers are _____​

Answer 1

$\huge{\underline{Required \: Answer:-}}$

${\purple{We \: have:}}$

Sum of the numbers = 16.

The difference of their squares is 32.

To FinD:

The Two numbers are _____?

$\underline{Explanation:}$

Let us assume the two no.s be a and b.

Then according to question, framing equations based on the given data:

Equation (1)

a + b = 16

Equation (2)

a² - b² = 32 (assuming a>b)

Consider the first equation, b can be written as:

⇛ b = 16 - a

Now substituting value of b in the 2nd equation,

⇛ a² - (16 - a)² = 32

⇛ a² - (256 + a² - 32a) = 32

⇛ a² - 256 - a² + 32a - 32 = 0

⇛ 32a - 288 = 0

⇛ a = 9

$\pink{Then,}$

⇛ b = 16 - 9

⇛ b = 7

$\red{Hence,}$

The required numbers whose sum is 16 and difference of squares is 32 are $\boxed{\green{9}}$ and $\boxed{\red{7}}$

Answer 2

Equation (1)

a + b = 16

Equation (2)

a² - b² = 32 (assuming a>b)

Consider the first equation, b can be written as:

⇛ b = 16 - a

Now substituting value of b in the 2nd equation,

⇛ a² - (16 - a)² = 32

⇛ a² - (256 + a² - 32a) = 32

⇛ a² - 256 - a² + 32a - 32 = 0

⇛ 32a - 288 = 0

⇛ a = 9

Then,

⇛ b = 16 - 9

⇛ b = 7

Hence,