Question

if a= 1 ÷ 7-4√3 and b= 1 ÷ 7+4√3, then find the value of


a³+ b³

Answer 1

Answer:

Step-by-step explanation:

a = 1/( 7 -4√3) = ( 7 + 4√3)/( 7-4√3)(7+4√3)

= (7+ 4√3)/(7² -(4√3)²) = 7 + 4√3

similarly ,

b = 1/( 7 +4√3) = ( 7 - 4√3)

now ,

a + b = ( 7 + 4√3) + ( 7-4√3) = 14

also b = 1/a

hence,

a³ + b³ = a³ + 1/a³ = ( a + 1/a)³ -3a×1/a( a +1/a) = ( 14)³ - 3( 14 ) = 14 × ( 196- 3)

= 14 × 193 = 2702

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