o, p aee the €oots op equation कर-अठन फई़ेvalue 0L

1.	o, p aee the €oots op equation कर-अठन फई़ेvalue 0L A%+
Answer» Alpha and beta are the roots of x² -2x + 4 = 0 α + β = 2 αβ = 4 now, (α)^5 + ( β)^5 = { α² + β² }{ α³ + β³ } - α²β³ - β².α³ = {( α + β)² - 2αβ} {(α + β)³ - 3αβ(α + β)} - α²β²(α + β) = {(2)²-2(4)}{(2)² - 3(4)(2)} -(4)²(2) = {4 - 8)(8 - 24) - 32 = (-4)(-16) - 32 = 64 - 32 = 32

o, p aee the €oots op equation कर-अठन फई़ेvalue 0L A%+

Answer»

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

α + β = 2 αβ = 4

now, (α)^5 + ( β)^5 = { α² + β² }{ α³ + β³ } - α²β³ - β².α³

= {( α + β)² - 2αβ} {(α + β)³ - 3αβ(α + β)} - α²β²(α + β)

= {(2)²-2(4)}{(2)² - 3(4)(2)} -(4)²(2)

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

= (-4)(-16) - 32

= 64 - 32 = 32