Question

if a4+b4=a2b2 then a6+b6 is

Answer 1

Answer:

Step-by-step explanation:

It is given that,  

a⁴ + b⁴ = a²b²

rearranging this equation

⇒ a⁴ + b⁴ – a²b² = 0 …… (i)

Now, let’s solve for  

a⁶ + b⁶

= (a²)³ + (b²)³

= (a² + b²)[(a²)² - a²b² + (b²)²] …… [using algebraic formula: a³ + b³ = (a+b)(a²-ab+b²)]

= (a² + b²)[a⁴ - a²b² + b⁴]

= (a² + b²) * 0 ……. [substituting from (i)]

= 0  

Thus, a⁶ + b⁶ = 0

Answer 2

Answer:

0

Step-by-step explanation:

a4 + b4 = a2 b2 ⇒ a4 + b4 - a2 b2 = 0 ..... (i)

We know, a6 + b6 = ( a2 )3 + ( b2 )3

= ( a2 + b2 )( a4 - a2 b2 + b4 ) [Using identity]

= ( a2 + b2 ) × 0 = 0 [ From equation (i)]