if a=(3+√5)/2.Then find the value of a2+1/a2
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Answer:
7
Explanation:
a = 3 +∫5 / 2
Therefore, 1 / a = 2 / 3 + ∫5
= 2 * ( 3 - √5 ) / ( 3 + ∫5 ) * ( 3 - ∫ 5 )
= 2 * ( 3 - √5 ) / ( 3 ) ^ 2 - ( √5 ) ^ 2
= 3 - √5 / 2
a + 1 /a = 3+√5 /2 + 3-√5 /2
= 6 / 2
= 3
( a + 1 /a ) ^ 2 = a^2 + 1/a^2 + 2 (a)(1/a)
= ( a + 1 /a )^2 + 2 (a)(1/a)
= ( 3) ^2 - 2 = ( a + 1 /a )^2 + 2 (a)(1/a) - 2 ( Adding and subtracting 2 on both sides )
9 -2 = ( a + 1 /a )^2
= 7 .
Therefore, (a + 1/a)^2 = 7
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