Question

The sum of two numbers is 5 and the difference of their squares is 25. The difference of the two numbers will be ?

Please answer fast !!

Answer 1

Answer:

x + y = 5

x² - y² = 25

We know that x² - y² = (x + y)(x - y)

= (x + y)(x - y) = 25

= 5 * (x - y) = 25

= (x - y) = 5

Therefore, their difference is also 5.

Hope this helps you.

Answer 2

SOLUTION

GIVEN

• The sum of two numbers is 5

• The difference of their squares is 25

FORMULA TO BE IMPLEMENTED

We are aware of the identity that

$\sf{ {a}^{2} - {b}^{2} = (a + b)(a - b) }$

TO DETERMINE

The difference of the two numbers

EVALUATION

Let a and b are the two given numbers

Now the sum of two numbers is 5

a + b = 5 - - - - - (1)

Again the difference of their squares is 25

$\sf{ {a}^{2} - {b}^{2} = 25 \: \: \: - - - (2) }$

From Equation 2 we get

Using the above mentioned Identity

$\sf{(a + b)(a - b) = 25}$

Putting the value of a + b

$\sf{ \implies \: 5(a - b) = 25}$

Dividing both sides by 5

$\displaystyle \sf{ \implies \: (a - b) = \frac{25}{5} }$

$\displaystyle \sf{ \implies \: (a - b) = 5 }$

FINAL ANSWER

Hence the required value

$\boxed{ \: \: \displaystyle \sf{ \: (a - b) = 5 } \: }$

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