#### Question

The sum of two numbers is 48 and their product is 432. Find the numbers?

#### Solution

Given the sum of two numbers is 48

Let the two numbers be x and 48 – x also given their product is 432.

Hence x(48 - x) = 432

⇒ 48x - x^{2} = 432

⇒ 48x - x^{2} - 432 = 0

⇒ 𝑥2 - 48𝑥 + 432 = 0

⇒ 𝑥2 - 36𝑥 - 12𝑥 + 432 = 0 [By method of factorisation]

⇒ 𝑥(𝑥 - 36) - 12(𝑥 - 36) = 0

⇒ (𝑥 - 36)(𝑥 - 12) = 0

⇒ x = 36 or x = 12

∴ The two numbers are 12, 36.

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#### APPEARS IN

Solution The Sum of Two Numbers is 48 and Their Product is 432. Find the Numbers Concept: Solutions of Quadratic Equations by Factorization.