Question

if 3a + 1/3a=2√3
evaluate: 81a4+1/81a4​

Answer 1

Answer:

98

Step-by-step explanation:

The expansion of the identity (x+1/x)⁴ goes

x⁴+1/x⁴+4(x²+1/x²)+6

To find:- 9a²+1/9a²

(3a+1/3a)²=9a²+1/9a²+2

(2√3)²=9a²+1/9a²+2

hence, 9a²+1/9a²=12-2 [ Transposing ]

= 10

Therefore,

LHS= (3a+1/3a)⁴

RHS

= (3a)⁴+1/(3a)⁴+4(3a)²+1/(3a)²+6

(2√3)⁴ = 81a⁴+1/81a⁴+4(9a²+1/9a²)+6

144= 81a⁴+1/81a⁴+4(10)+6

81a⁴+1/81a⁴= 144-46. [ Transposing ]

= 98