Question

If y=5-25^(1/3)-5^(1/3) then value of y^3-15y^2+60y+40

Answer 1

you should do on your own this is not supposed to be done by us

Answer 2

Answer:

y³ - 15y² + 60y + 40 = 60

Step-by-step explanation:

y = 5 - ∛25 - ∛5

⇒ y - 5 = - ∛25 - ∛5

CUBE BOTH THE SIDES

(y - 5)³ = (- ∛25 - ∛5)³  

[USING THE IDENTITY ---- (a - b)³ = a³ - 3a²b + 3ab² - b³]

⇒ (y)³ - (3×y²×5) + (3×y×5²) - (5)³ =  

[-∛25)³ - (3×(-∛25)²×(∛5)] + [3×(-∛25)×(∛5)² - (∛5)³]

⇒ y³ - 15y² + 75y - 125 =  

- 25 - [3×(-∛25)²×(∛5)] + [3×(-∛25)×(∛5)²] - 5

⇒ y³ - 15y² + 75y - 125 = - 30 - { [3×(-∛25)²×(∛5)] + [3×(-∛25)×(∛5)²] }

[ IN  { [3×(-∛25)²×(∛5)] + [3×(-∛25)×(∛5)²] } TAKE OUT WHICH ARE COMMON, WHICH IS 3,-∛25 AND ∛5)]

⇒ y³ - 15y² + 75y - 125 = - 30 - { [3×(-∛25)×(∛5)] [(-∛25)-(∛5)] }

⇒ y³ - 15y² + 75y - 125 = - 30 - { [3×($-25^{1/3}$)×($5^{1/3}$)] [(-∛25)-(∛5)] }

[AS ∛5 IS $5^{1/3}$  OR 5 POWER 1/3]

⇒ y³ - 15y² + 75y - 125 = - 30 - { [3×((-5²)$^{1/3}$)×($5^{1/3}$)] [(-∛25)-(∛5)] }

⇒ y³ - 15y² + 75y - 125 = - 30 - { [3×($-5^{2/3}$)×($5^{1/3}$)] [(-∛25)-(∛5) }

[ AS ( - ∛25 - ∛5 ) IS ( y - 5 ) ]

⇒ y³ - 15y² + 75y - 125 = - 30 - { [3×($-5^{3/3}$)] [ y - 5 ] }

⇒ y³ - 15y² + 75y - 125 = - 30 - { [3×(-5)] [ y - 5 ] }

⇒ y³ - 15y² + 75y - 125 = - 30 - { [-15] [ y - 5 ] }

⇒ y³ - 15y² + 75y - 125 = - 30 - { -15 ( y - 5 ) }

⇒ y³ - 15y² + 75y - 125 = - 30 + 15 ( y - 5 )

⇒ y³ - 15y² + 75y - 125 = - 30 + 15y - 75

⇒ y³ - 15y² + 75y - 125 = 15y - 105

⇒ y³ - 15y² + 75y - 125 - 15y = - 105

⇒ y³ - 15y² + 60y - 125 = - 105

[ADD 165 ON BOTH THE SIDES TO GET + 40]

⇒ y³ - 15y² + 60y - 125 + 165 = - 105 + 165

⇒ y³ - 15y² + 60y + 40 = 60

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