Question

6. The difference between the squares of two consecutive numbers is 31. Find the numbers.
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Answer 1

Step-by-step explanation:

Let one of the numbers be x

therefore, 2nd no. = x+1

x²+ ( x+1 )² = 31

(x+ x+1 )² = 31

( 2x + 1 )² = 31

(2x)² + 2*2x*1 + 1² = 31

4x² + 4x + 1 = 31

4x² + 4x = 31-1

x²+ x = 30/16

x³ =

Answer 2

$\bf\huge\underline{Explanation :-}$

Given :

• Difference between the squares of two consecutive numbers = 31

To find :

• The numbers.

Solution :

Let the first number be 'x'

Since, the second number is consecutive to the first one, the second number will be '(x + 1)'

Difference between the squares of '(x + 1)' & 'x' is 31.

The equation formed will be -

$\sf\longrightarrow {(x + 1)}^{2} - {x}^{2} = 31$

By solving the equation,

$\sf\longrightarrow {x}^{2} + 2x + 1 - {x}^{2} = 31$

$\sf\longrightarrow 2x + 1 = 31$

$\sf\longrightarrow 2x = 31 - 1$

$\sf\longrightarrow 2x = 30$

$\sf\longrightarrow x = \dfrac{30}{2}$

$\sf\therefore x = 15$

Therefore, the first number (x) = 15

& the second number (x + 1) = 16

Hence, the two numbers are 15 and 16 respectively.