Question

x+y=4,xy=1 find the value of x​

Answer 1

Step-by-step explanation:

x+y = 4

(x+y)² = 4²

x²+2xy+y² = 16

x²+2×1+y² = 16

x²+2+y² = 16

x²+y² = 16-2

x²+y² = 14

(x+y)(x-y) = 14

4(x-y) = 14

x-y = 14/4

x-y = 7/2

x = 7/2+y

x+y = 4

7/2+y+y = 4

7/2+2y = 4

7/2+y = 4/2

7/2+y = 2

y = 2-7/2

y = 4-7/2

y = -3/2

We know that,

x = 7/2+y

x = 7/2+(-3/2)

x = 7/2-3/2

x = 4/2

x = 2

Answer 2

Answer:

2-√3 & 2+√3

Step-by-step explanation:

x=4-y........(from first equation)

Now (4-y)*y=1

or, y^2-4y+1=0

or, y= {4+√(16-4)}/2 & {4-√(16-4)}/2

= 2+√3 & 2-√3

Hence x= 4-(2+√3) & 4-(2-√3)

= 2-√3 & 2+√3

Alternative process ---

x-y = √(4^2 -4) = 2√3

Then proceed with elimination process with first equation by eliminating y. (just add them and divide with 2)