Question

the difference between two numbers is 12 are the different between their square is 408.find the number​

Answer 1

SOLUTION

GIVEN

The difference between two numbers is 12 and the difference between their square is 408

TO DETERMINE

The numbers

EVALUATION

Let x and y are the numbers

Now it is given that the difference between two numbers is 12

$\sf{x - y = 12 \: \: - - - - - (1)}$

Again it is also stated that the difference between their square is 408

$\sf{ {x}^{2} - {y}^{2} = 408}$

$\sf{ \implies \: (x + y)(x - y) = 408}$

$\sf{ \implies \:12 (x + y) = 408}$

$\sf{ \implies \: (x + y) = 34 \: \: \: - - - - (2)}$

Equation 1 + Equation 2 gives

2x = 46

$\implies \sf{x = 23}$

Again equation 1 gives

y = 23 - 12 = 11

Hence the required numbers are 23 & 11

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