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

Question

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

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Sadie 4 weeks 2021-08-22T23:16:31+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-22T23:18:25+00:00

    \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.

    0
    2021-08-22T23:18:27+00:00

    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 =

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