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6 March, 20:26

The square root of a number consisting of two digits isequal

to the sum of the digits and is less than the number obtainedby

interchanging the digits by 9. Find the number.

+2
Answers (1)
  1. 6 March, 22:38
    0
    81

    Step-by-step explanation:

    Let the digits that make up the number be a and b.

    Given that the square root of the number is equal to the sum of the digits.

    Then,

    √ (10a + b) = a + b

    Also given that the square root of the number is less than the number obtained by interchanging the digits by 9, then

    √ (10a + b) + 9 = 10b + a

    Since √ (10a + b) = a + b, then

    a + b + 9 = 10b + a

    a - a + 9 = 10b - b

    9b = 9

    b = 1

    since √ (10a + b) = a + b

    √ (10a + 1) = a + 1

    10a + 1 = (a + 1) ²

    10a + 1 = a² + 2a + 1

    a² + 2a - 10a + 1 - 1 = 0

    a² - 8a = 0

    a (a - 8) = 0

    a = 0 or a = 8

    Using a = 8 and b = 1,

    the number 10a + b = 10 (8) + 1 = 81.
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