Question

The difference between two numbers is 3 and the difference between their squares is 51 which are the numbers? *​

Answer 1

Answer:

10 and 7

Step-by-step explanation:

Let the numbers be x and y

ATQ,

$x - y = 3$

We also have

${x }^{2} - {y}^{2} = 51$

Using the algebraic identity

$(x + y)(x - y) = {x}^{2} - {y}^{2}$

We get

$(x + y)(x - y) = 51$

But we know that x - y = 3

$(x + y)(3) = 51$

Dividing both sides by 3

$x + y = 17$

Now we have the two equations

$x + y = 17 \\ x - y = 3$

Adding both these equations

$x + x + y - y = 17 + 3 \\ 2x = 20 \\ x = 10$

Substituting the value of x in the first equation

$(10) + y = 17 \\ y = 17 - 10 \\ y = 7$

x = 10; y = 7

Hence the two numbers are 10 and 7