Question

if a=5-5^(2/3)-5^(1/3) then prove that a^3 -15a^2+60a=20

Answer 1

Solution :-

➻ a = 5 - 5^(2/3) - 5^(1/3)

➻ (5 - a) = 5^(2/3) + 5^(1/3)

Cubing Both sides Now,

➻ (5 - a)³ = [5^(2/3) + 5^(1/3)]³

using :-

• (a - b)³ = a³ - b³ - 3ab(a - b) in LHS
• (a + b)³ = a³ + b³ + 3ab(a + b) in RHS

➻ 5³ - a³ - 3*5*a(5 - a) = {5^(2/3)}³ + {5^(1/3)}³ + 3*5^(2/3)*5^(1/3)[5^(2/3) + 5^(1/3)]

➻ 125 - a³ - 15a(5 - a) = 5² + 5 + 3*5^(2/3+1/3)[5 - a]

➻ 125 - a³ - 75a + 15a² = 30 + 15(5 - a)

➻ 125 - a³ - 75a + 15a² = 30 + 75 - 15a

➻ 125 - 105 - a³ - 75a + 15a + 15a² = 0

➻ - a³ + 15a² - 60a + 20 = 0

➻ a³ - 15a² + 60a = 20 (Proved).

Answer 2

Answer:

5

Step-by-step explanation:

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