If y = 5 - cube √ ( 25 ) - cube √ (5), then find the value of y ^ 3 - 15y ^ 2 + 60y + 40
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Given y =5-∛25-∛5
y-5 = -(∛25+∛5)
Cubing on both sides gives
⇒(y-5)³=-(∛25+∛5)³
⇒y³-125-15y(y-5) = -[25+5+15(5-y)] ∵-(∛25-∛5) = y-5
⇒y³-125-15y²+75y=- [105-15y]
⇒y³-15y²+60y+40=125-105
⇒y³-15y²+60y+40=20
∴y³-15y²+60y+40 = 180
y-5 = -(∛25+∛5)
Cubing on both sides gives
⇒(y-5)³=-(∛25+∛5)³
⇒y³-125-15y(y-5) = -[25+5+15(5-y)] ∵-(∛25-∛5) = y-5
⇒y³-125-15y²+75y=- [105-15y]
⇒y³-15y²+60y+40=125-105
⇒y³-15y²+60y+40=20
∴y³-15y²+60y+40 = 180
Shreyansh2308:
thanks for putting your efforts on my question but the options didn't have 180 in them and also the ans is 60
yes a bit mistake
no problem
Answered by
18
answer of this question is must be 60
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amazing ans. bro
you helped me a lot
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