Math, asked by Ramu111, 1 year ago

If alpha and beta are the roots of x2-2x+4=0 then alpha5+beta5 =

Answers

Answered by abhi178

alpha and beta are the roots of
x² -2x + 4 = 0

alpha + beta = 2
alpha.beta = 4

now,
(alpha)^5 + ( beta )^5

{ alpha² + beta² }{ alpha³ + beta³ } -alpha².beta³ -beta².alpha³

={( alpha + beta)² -2alpha.beta} {(alpha + beta )³ -3alpha.beta(alpha+beta)} -alpha².beta²(alpha +beta)

={(2)²-2(4)}{(2)² - 3(4)(2)} -(4)²(2)

={4-8)(8 - 24) - 32

=(-4)(-16) -32

=64 - 32 = 32

Ramu111: You're answering my questions so speed you are so genious

abhi178: thanks ,

Ramu111: How we get that formula a^5+b^5

abhi178: multiply (a² + b²) and (a³ + b³) , then subtract (a²b³ + b²a³)

abhi178: if you want to detail comes to my private chat

Ramu111: ok

Ramu111: how to come

Answered by yenumulapellivishnut

Answer:

32.0

Step-by-step explanation:

alpha and beta are the roots of

x² -2x + 4 = 0

alpha + beta = 2

alpha.beta = 4

now,

(alpha)^5 + ( beta )^5

{ alpha² + beta² }{ alpha³ + beta³ } -alpha².beta³ -beta².alpha³

={( alpha + beta)² -2alpha.beta} {(alpha + beta )³ -3alpha.beta(alpha+beta)} -alpha².beta²(alpha +beta)

={(2)²-2(4)}{(2)² - 3(4)(2)} -(4)²(2)

={4-8)(8 - 24) - 32

=(-4)(-16) -32

=64 - 32 = 32

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