If x + y = 4, x2 + y2 = 14 and x > y, then the correct

Home » Aptitude » Algebra » Question

If x + y = 4, x² + y² = 14 and x > y, then the correct value of x and y is :

1. 2 + √3 , 2 – √3
2. 2 – √2 , √3
3. 3, 1
4. 2 + √3 , 2√2

Correct Option: A

x + y = 4 --- (i)
x² + y² = 14 --- (ii)
∴ (x + y)² = x² + y² + 2xy
⇒ 16 = 14 + 2xy
⇒ 2xy = 16 – 14 = 2
⇒ xy = 1 --- (iii)
∴ (x – y)² = (x + y)² – 4xy
= (4)² – 4 = 16 – 4 = 12
⇒ x – y = √12 = 2 √3 --- (iv)
∴ On adding equations (i) and (iv)

x + y = 4

x − y = 2√3

____________

2x = 4 + 2√3

⇒ x = 2 + √3

From equation (i),
2 + √3 + y = 4
⇒ y = 4 – 2 – √3 = 2 – √3