Question

x+y = 4 ,xy=2, y+z=5, yz=3, z+x =6 and zx = 4 then find the value of x² + y² + z²-3xy​

Answer 1

Step-by-step explanation:

x+y = 4 a

xy=2. b

y+z=5. c

yz=3. d

z+x =6 e

a + c + e

x + y + y + z + z + x = 15

2x + 2y + 2z = 15

x + y + z = 7.5. f

b + d

xy + yz = 5

y ( x + z ) = 5

x + z = 5 / y. g

put g in f

5 / y + y = 7.5

5y + y / y² = 7.5

6y / y² = 7.5

1/y = 7.5/6

y = 0.8

xy = 2

x = 2.5

yz = 3

z = 3.75

x² + y² + z²-3xy

2.5²+0.8²+3.75²-3*(2.5)(0.8)

20.9525−6

14.9525