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The Difference of Two Numbers is 3 and the Difference of Their Squares is 69. Find the Numbers. - Mathematics

Sum

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

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Solution

Let one number = x

Second number = x + 3 [Difference of two numbers is 3]

According to the statement :

(x + 3)2 - (x)2 = 69

⇒ (x)2 + (3)2 + 2 × x × 3 - x2 = 69 

⇒ x2 + 9 + 6x - x2 = 69

⇒ 6x = 69 - 9

⇒ 6x = 60

⇒ x = `60/6`

⇒ x = 10

One number = 10

Second number = x + 3 = 10 + 3 = 13

Concept: Solving Linear Inequations
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APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 14 Linear Equations in one Variable
Exercise 14 (B) | Q 16 | Page 169
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