Question

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

Answer 1

Answer:

let no be a+b = 16

a2,-b2 =32

formula of a2-b2 is(a+b)(a-b)

so 16(a_b) =32

so a-b = 2

a+b=16

a-b=2

solving a=9

b=7

Answer 2

Required Answer:-

We have:

• Sum of the numbers = 16.
• The difference of their squares is 32.

To FinD:

• The Two numbers are _____?

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

Then,

⇛ b = 16 - 9

⇛ b = 7

Hence:-

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