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Required Answer:-

Given:

  • X + y = 16
  • xy = 63

To find:

  • The VALUE of x and,
  • The value of y.

Solution:

Given that,

➡ x + y = 16 ....(i)

➡ xy = 63

Squaring both sides of equation (i), we get,

➡ (x + y)² = 16²

➡ x² + y² + 2xy = 256

➡ x² + y² + 2 × 63 = 256

➡ x² + y² = 256 - 126

➡ x² + y² = 130

Subtracting 2xy from both sides, we get,

➡ x² - 2xy + y² = 130 - 2xy

➡ (x - y)² = 130 - 126

➡ (x - y)² = 4

➡ (x - y) = √4

➡ x - y = ±2 .....(ii)

So, when x + y = 16 and x - y = 2,

➡ x + y + x - y = 16 + 2

➡ 2x = 18

➡ x = 9

Also,

y = 16 - x

= 16 - 9

= 7

Therefore,

x = 9,

y = 7

Again, when x + y = 16 and x - y = -2,

➡ x + y + x - y = 16 - 2

➡ 2x = 14

➡ x = 7

Also,

y = 16 - x

= 16 - 7

= 9

So,

x = 7,

y = 9

Hence, there are TWO solutions for this question.

  1. x = 9 and y = 7,
  2. x = 7 and y = 7


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