Prove, using mathematical induction, that the given property of the Fibonacci numbers is true [F(n+1)]2 =[F(n)]2+F(n−1)∗F(n+2) foran≥2 Where Fibonacci numbers are defined by the recurrence relation F(1) = 1 F(2) = 1 F(n) = F(n − 1) + F(n − 2)

Write a function balancechemical to balance chemical reactions by solving a linear set of equations. the inputs arguments are: reagents: symbols of reagents in string row array products: symbols of products in string row array elements: elements in the reaction in string row array elcmpreag: elemental composition of reactants in two dimensional numeric array elcmpprdcts: elemental composition of prducts in two dimensional numeric array hint: the first part of the problem is setting up the set of linear equations that should be solve. the second part of the problem is to find the integers from the solution. one way to do this is to mulitiply the rational basis for the nullspace by increasing larger integers until both the left-and right-side integers exist. for example, for the reaction that involves reacting with to produce and : reagents=["ch4", "o2"]; products =["co2", "h2o"]; elements =["c","h", "o"] elcmpreag=[1,4,0;