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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Question

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

KnowledgeBoat · Accepted 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 = ⇒ x \+ y = 23 .............(2) Adding (1) and (2) ⇒ (x \- y) \+ (x \+ y) = 3 \+ 23 ⇒ x \- y \+ x \+ y = 26 ⇒ 2x = 26 ⇒ x = ⇒ x = 13 Using eq (2) ⇒ y = 23 \- 13 ⇒ y = 10 Hence, the numbers are 13 and 10.

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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