Question

Find the numbers if the sum of its square is 244 and difference of greater to smaller number is 2.

Answer 1

Answer :-

The greater number is - 10 or 12 and smaller number is - 12 or 10

Explanation :-

Given :-

Differen between greater and smaller number is 2

Sum of its squares = 244

To find :-

Numbers

Solution :-

Let the greater number be x and smaller number be y

Difference between greater number and smaller number = 2

⇒ x - y = 2

We can write value of x in terms of y

⇒ x = 2 + y ---(1)

Square of greater number = (x)² = x²

Square of smaller number = (y)² = y²

Sum of its squares = 244

⇒ x² + y² = 244

Now substitute value x = y + 2 in the above equation

⇒ (2 + y)² + y² = 244

⇒ 2² + y² + 2(2)(y) + y² = 244

⇒ 4 + y² + 4y + y² = 244

⇒ 2y² + 4 + 4y = 244

⇒ 2y² + 4y = 244 - 4

⇒ 2y² + 4y = 240

⇒ 2y² + 4y - 240 = 0

⇒ 2(y² + 2y - 120) = 0

⇒ y² + 2y - 120 = 0/2

⇒ y² + 2y - 120 = 0

Split the middle term

⇒ y² + 12y - 10y - 120 = 0

⇒ y(y + 12) - 10(y + 12) = 0

⇒ (y + 12)(y - 10) = 0

⇒ y + 12 = 0 or y - 10 = 0

⇒ y = - 12 or y = 10

Both y = - 12 or 10

(i) Substititute y = - 12 in (1)

⇒ x = 2 + y

⇒ x = 2 + ( - 12)

⇒ x = 2 - 12

⇒ x = - 10

(ii) Substititute y = 10 in (1)

⇒ x = 2 + y

⇒ x = 2 + 10

⇒ x = 12

So. x = - 10 or 12

So, the greater number is - 10 or 12 and smaller number is - 12 or 10

Verification :-

When x = - 10 and y = - 12

⇒ x² + y² = 244

⇒ (-10)² + (-12)² = 244

⇒ 100 + 144 = 244

⇒ 244 = 244

When x = 12 and y = 10

⇒ x² + y² = 244

⇒ (12)² + (10)² = 244

⇒ 100 + 144 = 244

⇒ 244 = 244