Question

What are the numbers where their difference is 2 and the product is 80

Answer 1

Given :-

• The difference of numbers is 2 and its product is 80.

To find :-

• Required numbers

Solution :-

Let the required numbers be x and y

• According to first condition

→ Difference between two numbers is 2

→ x - y = 2

→ x = 2 + y ---(i)

• According to second condition

→ Product of two numbers

→ xy = 80

• Put the value of x

→ (2 + y)y = 80

→ 2y + y² = 80

→ y² + 2y - 80 = 0

• Split middle of term

→ y² + 10y - 8y - 80 = 0

→ y(y + 10) - 8(y + 10) = 0

→ (y + 10)(y - 8) = 0

Either

→ y + 10 = 0

→ y = - 10

Or

→ y - 8 = 0

→ y = 8

Put the values of y in equation (i)

→ x = y + 2

→ x = - 10 + 2 (y = - 10)

→ x = - 8

Now

→ x = y + 2

→ x = 8 + 2

→ x = 10

Hence,

• Required numbers

→ x = - 8 or 10

→ y = - 10 or 8

Answer 2

Step-by-step explanation:

Let the required numbers be 'R' and 'S'.

According to first statement,

● The numbers where their differences is 2.

↪ R - S = 2

↪ R = 2 + S ----(i)

According to second statement,

● The product of numbers is 80.

↪ R × S = 80 ---(ii)

Put the value of eqn. (i) in eqn. (ii),

↪ 2 + S × S = 80

↪ 2S + S² = 80

↪ S² + 2S - 80 = 0

↪ S² + 10S - 8S - 80 = 0

↪ S(S + 10) - 8(S + 10) = 0

↪ (S + 10) (S - 8) = 0

↪ S = -10 & S = 8

Now,

Put S = -10 in eqn. (i),

↪ R = 2 + (-10)

↪ R = -8

Put S = 8 in eqn. (i),

↪ R = 2 + 8

↪ R = 10

Therefore,

Required numbers are,

• R = -8 & 10
• S = -10 & 8