Question

if a^2-3a+1=10 find a^3+1/a^3​

Answer 1

Given :-

• a² - 3a + 1 = 0

To Find :-

• (a³ + 1/a³) = ?

Formula used :-

• (a + b)³ = a³ + b³ + 3ab(a + b)

Solution :-

→ a² - 3a + 1 = 0

Taking a common ,

→ a (a - 3 + 1/a) = 0

→ (a - 3 + 1/a) = 0

→ (a + 1/a) = 3 ------------- Equation (1)

Cubing Both sides now,

→ (a + 1/a)³ = 3³

using (a + b)³ = a³ + b³ + 3ab(a + b) in LHS,

→ a³ + 1/a³ + 3 * a * 1/a ( a + 1/a) = 27

→ a³ + 1/a³ + 3( a + 1/a) = 27

Putting value of Equation (1) now,

→ a³ + 1/a³ + 3*3 = 27

→ (a³ + 1/a³) = 27 - 9

→ (a³ + 1/a³) = 18 (Ans.) .

Answer 2

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$\huge\tt{GIVEN:}$

• a^2-3a+1=10

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$\huge\tt{TO~FIND:}$

• a^3+1/a^3

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$\huge\tt{SOLUTION:}$

↪ a (a - 3 + 1/a) = 0

↪ (a - 3 + 1/a) = 0

↪(a + 1/a) = 3 _____(EQ.1)

↪ (a + 1/a)³ = 3³

↪a³ + 1/a³ + 3 * a * 1/a ( a + 1/a) = 27

↪a³ + 1/a³ + 3( a + 1/a) = 27

↪a³ + 1/a³ + 3*3 = 27

↪(a³ + 1/a³) = 27 - 9

↪ (a³ + 1/a³) = 18

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