Answer:
Multiply both equations to get a new equation:(a2+(1/a2))•(a3+(1/a3))=5•82. To open brackets, multiply each of the terms in the first brackets with each term of the second bracketa5+(a2/a3)+(a3/a2)+(1/a5)=403. Isolate a5+(1/a5) in one side of the expressiona5+(1/a5)=40-((a3/a2)+(a2/a3))4. Simplify fractions on the right expressiona5+(1/a5)=40-(a+(1/a))
Step-by-step explanation:
Lets solve this problem:Now assuming you'll know the expressions:a2+b2 =(a+b)2- 2ab -------------------------- (eq. 1) a3+b3= (a+b)3-3ab(a+b)---------------------- (eq. 2) Follow the steps given by Raquel and you arrive at a5 +(1/a5) = 40 -(a+(1/a)) , ------------------------------- (eq. 3)To find a+1/a;a2 + 1/a2 = 5a2 + 1/a2= (a+ 1/a)2 - 2(a *1/a) = (a + 1/a)2 - 2Which implies;(a+1/a)2 -2 = 5Isolating a + 1/a, we get (a + 1/a)2 = 7 ----------------------------------- (eq. 4)Next, a3 + 1/a3 = 8from the eqn 2;a3 + 1/a3 = (a +1/a)3 - 3( a*1/a)(a + 1/a) = (a+1/a)3 - 3(a + 1/a)On the RHS, we will take out (a +1/a) and then interchanging LHS and RHS we get ;(a +1/a) ((a+1/a)2 -3) = a3 +1/a3(a +1/a) ((a+1/a)2 -3) = 8 ------------------- ( a3 +1/a3 = 8)(a+1/a)(7 - 3) = 8 -------------------- ( from eq.4 we know (a+ 1/a)2 = 7)(a + 1/a) (4) = 8(a + 1/a) = 8/4(a+1/a) = 2 ---------------------------------- (eq .5)put a + 1/a = 2 in eq.3We geta5 + 1/a5 = 40 -2a5 + 1/a5 = 38
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