Question

if a^4+b^4=a^2+b^2 proove a^6+b^6=0​

Answer 1

Heya! Mate

We are given that

a⁴ + b⁴ = a²b²

What we need to prove is

a⁶ + b⁶ = 0

Here I your proof

a⁶ + b⁶ can be written as (a²)³ + (b²)³

[Since x³ + y³ = (x + y)(x² + y² - xy)]

Therefore

=> (a²)³ + (b²)³ = (a + b)(a⁴ + b⁴ - a²b²)

[given a⁴ + b⁴ = a²b²]

=> (a²)³ + (b²)³ = (a + b)(a²b² - a²b²)

=> a⁶ + b⁶ = (a + b)(0)

=> a⁶ + b⁶ = 0

Thus proved...