Question

The difference of two numbers is 7. The product of the two numbers is 60. What are the two numbers?

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

5 and 12

Step-by-step explanation:

Let the two numbers be x and y.

A.T.Q.,

• Difference of two numbers = 7

→ x - y = 7

From this, we get

→ x = 7 + y ...(1)

Also,

• Product of two numbers = 60

→ xy = 60 ...(2)

Putting (1) in (2), we get

→ (7 + y)(y) = 60

→ (y)(7) + (y)(y) = 60

→ 7y + y² = 60

→ y² + 7y - 60 = 0

Using Middle Term Factorisation.

→ y² + 12y - 5y - 60 = 0

→ y(y + 12) - 5(y + 12) = 0

→ (y + 12)(y - 5) = 0

To Find zeroes, these factors should be equal to zero.

Using zero product rule.

→ (y + 12) = 0 or (y - 5) = 0

→ y = - 12 or y = 5

y is a natural number. It can't be negative.

Hence, y = 5

Putting this value in (1), we get

→ x = 7 + 5

→ x = 12

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Hence, the two numbers are 5 and 12.

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