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Two Number Differ by 4 and Their Product is 192. Find the Numbers? - Mathematics

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Question

Two number differ by 4 and their product is 192. Find the numbers?

Solution

Let two required numbers be and (x + 4)

Then according to question

x(x + 4) = 192

x2 + 4x - 192 = 0

x2 + 16x - 12x - 192 = 0

x(x + 16) - 12(x + 16) = 0

(x + 16)(x - 12) = 0

x + 16 = 0

x = -16

Or

x - 12 = 0

x = 12

Since, being a number,

Therefore,

When x = -16 then

x + 4 = -16 + 4 = -12

And when x = 12 then

x + 4 = 12 + 4 = 16

Thus, two consecutive number be either 12, 16 or -16, -12.

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APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.7 | Q: 26 | Page no. 52
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.7 | Q: 26 | Page no. 52
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Two Number Differ by 4 and Their Product is 192. Find the Numbers? Concept: Solutions of Quadratic Equations by Factorization.
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