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If (a+1/a) =4, find the value of (a cube +1/a cube)​

User Scampbell
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1 Answer

2 votes

Answer:

a=2+√3 or a=2−√3

Explanation:

Multiply all terms by a and cancel:

aa+1=4a ∴ (Simplify both sides of the equation)

a2+1−4a=4a−4a ∴ (Subtract 4a from both sides)

a2−4a+1=0

For this equation: a=1, b=-4, c=1

1a2+−4a+1=0

a = −b ± √b2 − 4ac2a divided by 2a ⇒(Use quadratic formula with a=1, b=-4, c=1)

−(−4) ± √(−4) 2−4 (1) (1) /2 (1)

a=4±√12/2

a=2+√3 or a=2−√3

a=2+√3 or a=2−√3

User AGeek
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