#### 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} - x^{2} = 88

4x^{2} - 20x + 25 - x^{2} - 88 = 0

3x^{2} - 20x - 63 = 0

3x^{2} - 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, *x *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?

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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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