Question

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

Answer 1

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) .

[Note :- if we want to use same value as 12 we have to take sum as 12. If we want to use difference , we have to take it as 18 . and, if we want to use difference as 12, we have to take Multiplication as +45 . for all these three our answer will remain same. ]

Answer 2

SOLUTION

TO DETERMINE

The pair of integer in which multiplication is 45 and difference is 12

EVALUATION

Here it is given that for the given pair of integers difference is 12

Let the integers are x and x + 12

Now their multiplication is 45

So by the given condition

$\sf{x(x + 12) = 45}$

$\sf{ \implies \: {x}^{2} + 12x = 45}$

$\sf{ \implies \: {x}^{2} + 12x - 45 = 0}$

$\sf{ \implies \: {x}^{2} + 15x - 3x - 45 = 0}$

$\sf{ \implies \: x(x + 15) - 3(x + 15)= 0}$

$\sf{ \implies \: (x + 15) (x - 3)= 0}$

$\sf{ \implies \:x = - 15 \: , \: 3}$

When x = - 15 the pair of integers are - 15 , - 3

When x = 3 the pair of integers are 3 , 15

FINAL ANSWER

Hence the required pair of integers are

• - 15 , - 3

• 3 , 15

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