CBSE Class 9 Answered

x⁴  + y⁴ -8x² y² = x⁴  + y⁴ -2x² y² - 6x² y²

                          = (x² +y²)  - 6x² y²            .................eqn (1)

Now,

 x = 3+32    ⇒ x² = 3 + 18 + 6 6 = 21 + 6 6

y =3 - 32    ⇒ y² = 3 + 18 - 6 6 = 21 - 6 6

On sunbstitution in eqn (1)

x⁴  + y⁴ -8x² y² = (x²  - y²)  - 6x² y²           

                         = (21 + 6 6 - 21 + 6 6) - 6(21 + 6 6)(21 - 6 6)

                         = 126 - 6 ((21)² - (6 6)²)

Compute this to get the final answer.