Solve the given question:
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Answer:
Given, y² + 1/y² = 23
⇒ (y + 1/y)² - (2 × y × 1/y) = 23
⇒ (y + 1/y)² - 2 = 23
⇒ (y + 1/y)² = 23 + 2
⇒ (y + 1/y)² = 25
⇒ y + 1/y = - 5,
where we take the negative value only.
∴ y³ + 1/y³
= (y + 1/y)³ - (3 × y × 1/y)(y + 1/y)
= (- 5)³ - {3 × (- 5)}
= - 125 + 15
= - 110
Identity rule :
a³ + b³ = (a + b)³ - 3ab(a + b)
Answered by
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Step-by-step explanation:
y²+1/y²=14
=>(y+1/y)²-2=14
=>(y+1/y)²=16
=>y+1/y=4
y³+1/y³
=((y+1/y)(y²-1+1/y²)
=(4)(14-1)
=4×13
=52
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