Question

(iii) x2 - y2 – z?, y2 – 22 – x², z2 – x2 - y2 ​

Answer 1

Step-by-step explanation:

x

2

+y

2

+z

2

=xy+yz+zx=a

2

......... (i)

3x−y+z=a

3

........... (ii)

⟹2(x

2

+y

2

+z

2

)=2a

2

....... (iii)

2(xy+yz+zx)=2a

2

........ (iv) From (i)

Subtracting (iii) and (iv):−

2(x

2

+y

2

+z

2

)−2xy−2yz−2zx=0

x

2

+y

2

−2xy+y

2

+z

2

−2yz+z

2

+x

2

−2zx=0

(x−y)

2

+(y−z)

2

+(z−x)

2

=0

This is possible iff,

x−y=0,y−z=0,z−x=0

i.e. x=y,y=z,z=x

i.e. x=y=z=k (let)

In equation (ii)

3k−k+k=a

3

⇒k=

3

a

Hence, x=y=z=

3

a