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Mathematics

The difference of two numbers is 3 and the difference of their squares is 69. Find the numbers.

Linear Eqns One Variable

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Answer

Let the two numbers be x and y.

So,

x - y = 3 ………….(1)

And,

x2 - y2 = 69

Using the formula

[∵ (x2 - y2) = (x - y)(x + y)]

⇒ (x - y)(x + y) = 69

Using eq (1), we get

⇒ 3(x + y) = 69

⇒ x + y = 693\dfrac{69}{3}

⇒ x + y = 23 ………….(2)

Adding (1) and (2)

⇒ (x - y) + (x + y) = 3 + 23

⇒ x - y + x + y = 26

⇒ 2x = 26

⇒ x = 262\dfrac{26}{2}

⇒ x = 13

Using eq (2)

⇒ y = 23 - 13

⇒ y = 10

Hence, the numbers are 13 and 10.

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