JEE Advanced Model Paper 18 with solutions for online practice

x4+y4+z4 + 1 - 4xyz = 0
⇒ x4+y4−2x2y2+z4 + 1 - 2z2 + 2x2y2 + 2z2 - 4xyz = 0
⇒ (x2−y2)2 + (z2−1)2 + 2 (xy−z)2 = 0
⇒ z2 = 1
xy = z and x2 = y2
z = 1 ⇒ x = 1 and y = 1
x = - 1 , y = - 1
z = - 1 ⇒ x = - 1 and y = 1
x = 1 , y = - 1
A (1 , 1 , 1) , B (- 1 , - 1 , 1) , C (- 1 , 1 , - 1) and D (1 , - 1 , - 1)

→

AB

= −2

^

i

−2

^

j

→

AC

= −2

^

i

−2

^

k

→

AD

= −2

^

j

−2

^

k

Volume =

1

6

|

−2	−2	0
−2	0	−2
0	−2	−2

| =

1

6

(8 + 8) =

8

3