Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the multiplicative inverse of ( 2 +1 )²⁰ ?

Step-by-step solution

The multiplicative inverse of ( 2 +1 )²⁰ is 1 ( 2 +1 )²⁰ . Rationalizing the base gives 1 2 +1 = 2 -1 ( 2 +1 ) ( 2 -1 ) = 2 -1 . Thus, 1 ( 2 +1 )²⁰ = ( 2 -1 )²⁰ . Given that v = ( 2 -1 )¹⁰ . Squaring both sides yields v^2 = ( 2 -1 )²⁰ . Therefore, the multiplicative inverse of ( 2 +1 )²⁰ is v^2 . Answer: v^2