Question

two consecutive numbers are squared. the difference of their squares is 81. then the two numbers are?

Answer 1

according to question,
(x+1)^2 -(x)^2=81
=x^2+1+ 2x -x^2=81
1+2x=81
2x=81-1=80
x=80÷2
=40
therefore,two consecutive nos. are
x=40
x+1=40+1
=41

Answer 2

The correct answer is 40 and 41.

Given: Difference of squares of two consecutive numbers is 81.

To Find: The two numbers.

Solution:

Let the first number = x.

The second number will be = x+1 (as both numbers are consecutive).

$(x+1)^{2} -x^{2} =81$

$x^{2} +2x+1-x^{2} =81$

2x + 1 = 81

2x = 80

x = 40

The first number = x = 40.

The second number = x+1 = 40+1 = 41

Hence, the two numbers are 40 and 41.

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