Question

plz solve this question​

Answer 1

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a⁴ + b⁴ = ( a² + b² )² - 2(ab)²

( a² + b² ) = ( a + b )² - 2ab

ab = 2√3 And ( a + b ) = ?

In Order To find ( a + b ) we use A.M and G.M

A.M ≥ G.M

(a + b)/2 ≥ (ab)½

(a + b) ≥ 2 (ab)½

(a + b) ≥ 2 (2√3)½

On Taking Minimum value of (a + b) we have

(a + b) = 2(2√3)½

So, (a² + b²) = {2(2√3)½}² - 2(2√3)

(a² + b²) = 8√3 - 4√3

(a² + b²) = 4√3

So,

a⁴ + b⁴ = (4√3)² - 2(2√3)²

a⁴ + b⁴ = 48 - 24

a⁴ + b⁴ = 24