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The Difference of Squares of Two Number is 88. If the Larger Number is 5 Less than Twice the Smaller Number, Then Find the Two Numbers. - CBSE Class 10 - Mathematics

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Question

The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.

Solution

Let the smaller numbers be x

Then according to question,

The larger number be = 2x - 5, then

(2x - 5)2 - x2 = 88

4x2 - 20x + 25 - x2 - 88 = 0

3x2 - 20x - 63 = 0

3x2 - 27x + 7x - 63 = 0

3x(x - 9) + 7(x - 9) = 0

(x - 9)(3x + 7) = 0

x - 9 = 0

x = 9

Or

3x + 7 = 0

3x = -7

x = -7/3

Since, being a positive integer so, x cannot be negative,

Therefore,

When x = 9 then larger number be

2x - 5 = 2(9) - 5 = 18 - 5 = 13

Thus, two consecutive number be either 9, 13.

  Is there an error in this question or solution?

APPEARS IN

Solution The Difference of Squares of Two Number is 88. If the Larger Number is 5 Less than Twice the Smaller Number, Then Find the Two Numbers. Concept: Solutions of Quadratic Equations by Factorization.
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