if y2+1/y2=23, find the value of y3+1/y3, using only negative value of y+1/y
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Answered by
60
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)
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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)
#MarkAsBrainliest
Answered by
4
Answer:
Step-by-step explanation:
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