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

- 3, 1
- 2-√2, √3
- 2+√3, 2-√3
- 2+√3, 2√2

**Answer: (3) 2 + √3, 2 – √3**

**Explanation:-**

X + Y = 4 ……………………. (1)

Square on both side,

(X + Y)² = 4²

X² + Y² + 2 X Y = 16

Put the value of X² + Y² = 14,

Then, 14 + 2 X Y = 16

2 X Y = 16 – 14

2 X Y = 2

X Y = 1

(X – Y)² = X² + Y² – 2 X Y

Put the value of X Y = 1 & X² + Y² = 14,

Then, (X – Y)² = 14 – 2

(X – Y)² = 12

Square root on both side,

X – Y = 2√3 …………………..(2)

Add equation (1) & (2),

X + Y + X – Y = 4 + 2√3

2 X = 2 (2 + √3)

X = 2 + √3

Now, put the value of X = 2 + √3 in equation (1),

Then, 2 + √3 + Y = 4

Y = 4 – 2 – √3

Y = 2 – √3

Then, the value of X = X = 2 + √3 & Y = 2 – √3

Hence, the correct answer is option (3) 2 + √3, 2 – √3.