Question

if a,b are roots of x²-2x+4=0 find the value of a⁶+b⁶​

Answer 1

Answer:

128

Step-by-step explanation:

α + β = 2

αβ = 4

α2 + β2 = (α + β)2 – 2αβ

= 4 – 8

= – 4

(α2 + β2)3 = α6 + β6 + 3 α2 β2 (α2 + β2)

– 64 = α6 + β6 + 3 * 16 (- 4)

α6 + β6 = 192 – 64

= 128

Answer 2

Answer:

128

Step-by-step explanation:

here sum of roots = 2 and product = 4

so a⁶ + b⁶ = (a² + b²)³ - 3a²b²(a²+ b²) (using x³ + y³ = (x+y)³ - 3xy(x+y) )

now a² + b² = sum² - 2 × product = 4-8 = -4

a²b² = 16

so, answer = -64 -3(16)(-4) = 128