Question

differences of two numbers is 8 and differences of their square is 208. find the number​

Answer 1

Answer:

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Answer 2

Given :-

Let two required numbers be a and b

According to the question,

a - b = 8

a^2 - b^2 = 8

Solution :-

a - b = 8 .........eq (1)

a^2 - b^2 = 208 ...........eq(2)

By using substitution method

Take equation 1

a - b = 8

a = 8 + b .......eq(3)

Now, subsitutes the value of

eq(3) in eq(2)

a^2 - b^2 = 208

(8 + b)^2 - b^2 = 208

64 + 16b + b^2 - b^2 = 208 ( using identity (a + b)^2 = a^2 + 2ab + b^2 )

16b = 208 - 64

16b = 144

b = 144/64

b = 9

The value of b = 9

Now, subsitute the value of b in eq(1)

a - b = 8

a - 9 = 8

a = 8 + 9

a = 17

The value of a = 17

The required numbers are 17 and 8