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The difference between the squares of two numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.

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This question has been taken from Book:- ML aggarwal, Avichal publication, class10th, quadratic equation in one variable, chapter 5, exercise 5.5
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The difference between the squares of two numbers is 45.

The square of the smaller number is 4 times the larger number.

Determine the numbers.
Question no.6 , ML Aggarwal, chapter 5, exercise 5.5, quadratic equation in one variable, ICSE board,

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1 Answer

  1. Let us consider the larger number be ‘x’

    Smaller number be ‘y’

    So according to the question,

    x2 – y2 = 45 … (i)

    y2 = 4x … (ii)

    Now substitute the value of y in equation (i), we get

    x2 – 4x = 45

    x2 – 4x – 45 = 0

    let us factorize,

    x2 – 9x + 5x – 45 = 0

    x(x – 9) + 5 (x – 9) = 0

    (x – 9) (x + 5) = 0

    So,

    (x – 9) = 0 or (x + 5) = 0

    x = 9 or x = -5

    When x = 9, then

    The larger number = x = 9

    Smaller number = y => y2 = 4x

    y = 4x = 4(9) = 36 = 6

    When x = -5, then

    The larger number = x = -5

    Smaller number = y => y2 = 4x

    y = 4x = 4(-5) = -20 (which is not possible)

    ∴ The value of x and y are 9, 6.

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