Question

if x = 2√3+√2
y= 2√3-√2,
then find x4 - y4​

Answer 1

Step-by-step explanation:

Given

x = 2√3+√2

y= 2√3-√2,

find x⁴ - y⁴

» we can write x⁴ - y⁴ as (x²)² - (y²)²

=> (x²-y²)*(x²+y²)........a²-b²=(a-b)*(a+b)

=> (x+y).(x-y)*(x²+y²)

-> ( x+y)² = x²+y² - 2xy

x²+y² = (x+y)² + 2xy

(x+y).(x-y)*[(x+y)² + 2xy]..........eq1

x+y = 4√3

x-y =2√2

(x+y)² => (4√3)²=>16*3=> 48

x*y = (2√3+√2)*(2√3-√2) => (4*3)-(2) => 12-2 = 10

puts the values in eq1

x⁴ - y⁴ = (x+y).(x-y)*[(x+y)² + 2xy]

= (4√3).(2√3)*[ 48 + 20]

= 24 * 68

= 1632

x⁴ - y⁴ = 1632

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