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Two Numbers Differ by 3 and Their Product is 504. Find the Number - CBSE Class 10 - Mathematics

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Question

Two numbers differ by 3 and their product is 504. Find the number

Solution

Let the two numbers be x and x - 3 given that x(x + 3) = 504

⇒ x2 + 3x - 504 = 0

⇒ x2 + 24x - 21x - 504 = 0

⇒ x(x + 24) - 21(x + 24) = 0

⇒ (x + 24)(x - 21) = 0

Therefore,

⇒ x + 24 = 0

⇒ x = -24

Or

⇒ x - 21 = 0

⇒ x = 21

Since, being a number,

Therefore,

When x = -24 then

x + 3 = -24 + 3 = -21

And when x = 21 then

x + 3 = 21 + 3 = 24

Thus, two consecutive numbers be either 21, 24 or -21, -24.

 

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Solution Two Numbers Differ by 3 and Their Product is 504. Find the Number Concept: Solutions of Quadratic Equations by Factorization.
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