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If a =3+√5/2 find a^2+1/a^2 |
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Answer» Step-by-step explanation: a= 2 3+
∴ a
= 3+ 5
2
On rationaliging the denominator , we get , a 1
= (3+ 5
)(3− 5
) 2(3− 5
)
= 9−5 6−2 5
= 4 6−2 5
= 2 3− 5
Also, (a+ a 1
) 2 =a 2 + a 2
1
+2 Substituting the values of a = a 1
, We get , `( 2 3+ 5
+ 2 3− 5
) 2 =(a 2 + a 2
1
+2) ∴a 2 + a 2
1
+2=( 2 3+ 5
+3− 5
) 2
=(3) 2 =9 ∴a 2 + a 2
1
=9−2=7. |
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