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If (x - 1)2 + (y - 2)2 = (x – 1) (y - 2), where x and y are integers, then value of 2x + 3y is:

If (x - 1)2 + (y - 2)2 = (x – 1) (y - 2), where x and y are integers, then value of 2x + 3y is: Correct Answer 8

Given,

(x - 1)2 + (y - 2)2 = (x – 1) (y - 2)

Concept:/Formula:

(x – y)2 = k2

(x – y) = k or (–k)

x = (k + y) or (y – k)

Calculation:

(x -1)2 + (y - 2)2 = (x – 1) (y - 2)

Taking,

⇒ (x – 1)2 = (x – 1) (y – 2)

⇒ (x – 1) = (y – 2)

⇒ x – y = -2 + 1

⇒ x – y = (-1)     ----(1)

Taking,

⇒ (y – 2)2 = (x – 1) (y – 2)

⇒ (y – 2) = (x – 1)

⇒ x – y = -2 + 1

⇒ x – y = (-1)     ----(2)

Let y = 2 and x = 1, then

⇒ 1 – 2 = (-1)

(-1) = (-1) (satisfied)

Now,

2x + 3y

⇒ 2 × 1 + 3 × 2

⇒ 2 + 6

⇒ 8

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