The difference between the squares of two consecutive numbers is 31. Find the numbers.
Linear Eqns One Variable
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Question

The difference between the squares of two consecutive numbers is 31. Find the numbers.

KnowledgeBoat · Accepted Answer

Let the two consecutive numbers be x, (x \+ 1). According to the question, the difference between the squares of two consecutive numbers is 31. ⇒ (x \+ 1)² \- x² = 31 Using the formula, [∵ (x \+ y)² = x² \+ y² \+ 2xy] ⇒ x² \+ 1² \+ 2 x 1 \- x² = 31 ⇒ x² \+ 1 \+ 2x \- x² = 31 ⇒ 1 \+ 2x = 31 ⇒ 2x = 31 \- 1 ⇒ 2x = 30 ⇒ x = ⇒ x = 15 Other number = (x \+ 1) = 15 \+ 1 = 16 Hence, the two consecutive numbers are 15 and 16.

Mathematics

The difference between the squares of two consecutive numbers is 31. Find the numbers.

Linear Eqns One Variable

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