Question

Write the pair of integer in which multiplication is (-45) and difference is 12.​

Answer 1

Answer:

Step-by-step explanation: Let the integers be x and y, such that x > y.

Given,

xy = 45             ↔(1)

x - y = 12

→ x = 12 + y       ↔(2)

By (2) in (1),

(12 + y)y = 45

⇒ 12y + y² = 45

⇒ y² + 12y - 45 = 0

⇒ y² - 3y + 15y - 45 = 0

⇒ y(y - 3) + 15(y - 3) = 0

⇒ (y + 15)(y - 3) = 0

⇒ y = -15, 3

When y = 15, x = -3

When y = 3, x = -15

Answer 2

Correct Question :- Write the pair of integer in which multiplication is (-45) and sum is 12. ?

Solution :-

Let us assume that, pair of integers have values x and y .

so,

→ x + y = 12

→ x = (12 - y) .

also,

→ x * y = (-45)

→ (12 - y) * y = (-45)

→ 12y - y² = (-45)

→ y² - 12y - 45 = 0

→ y² - 15y + 3y - 45 = 0

→ y(y - 15) + 3(y - 15) = 0

→ (y - 15)(y + 3) = 0

→ y = 15 or (-3) .

therefore,

if y = 15 => x = 12 - 15 = (-3)

if y = (-3) => x = 12 - (-3) = 15 .

Hence, pair of integer are (15, -3) or (-3, 15) .

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