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

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 \- x 2 = 31 Using the formula, [∵ (x \+ y) 2 = x 2 \+ y 2 \+ 2xy] ⇒ x 2 \+ 1 2 \+ 2 x 1 \- x 2 = 31 ⇒ x 2 \+ 1 \+ 2x \- x 2 = 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.

The ages of A and B are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their present ages.

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Find the number whose double is 45 greater than its half.

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Find a number such that when 5 is subtracted from 5 times the number, the result is 4 more than twice the number.

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Mathematics

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

Linear Eqns One Variable

Related Questions

The ages of A and B are in the ratio 7 : 5. Ten years hence, the ratio of their ages will be 9 : 7. Find their present ages.

Find the number whose double is 45 greater than its half.

Find a number such that when 5 is subtracted from 5 times the number, the result is 4 more than twice the number.