if a² -3a +1 =0 the find a²+1/ a²
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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
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