Question

if a² -3a +1 =0 the find a²+1/ a²
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Answer 1

Answer :

a² + 1/a² = 7

Solution :

• Given : a² - 3a + 1 = 0
• To find : a² + 1/a² = ?

We have ;

=> a² - 3a + 1 = 0

=> a² + 1 = 3a

=> (a² + 1)/a = 3

=> a²/a + 1/a = 3

=> a + 1/a = 3

Now ,

Squaring both the sides , we get ;

=> (a + 1/a)² = 3²

=> a² + (1/a)² + 2×a×(1/a) = 9

=> a² + 1/a² + 2 = 9

=> a² + 1/a² = 9 - 2

=> a² + 1/a² = 7

Hence ,

a² + 1/a² = 7