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in Quadratic Equations by (41.6k points)
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Two numbers differ by 4 and their product is 192. Find the numbers.

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Best answer

Let the larger number be ‘x’ 

Since the difference of two numbers is 4, 

Then the smaller number is (x – 4) 

Their product = x(x – 4) 

Given that product = 192 

∴ 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 or x = -12 

If x = 16, then x – 4 = 16 – 4 = 12 

then the numbers are 16 and 12. 

If x = – 12, then x-4 = – 12 – 4 = – 16 

then the numbers are – 12 and – 16.

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