if a =1/(7-4√3) and b=1/(7+4√3) find the value of a+b
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Answer:
Note that (a+1/a)^2 = a^2+1/(a^2)+2
a^2 = 7+4*sqrt(3)
1/a^2 = 7-4*sqrt(3)/(( 7-4*sqrt(3))*(7+4*sqrt(3)))
= 7-4*sqrt(3)/(49–48)=7-4*sqrt(3)
a^2+1/a^2 = 14
a^2+1/a^2 +2 = 16
so a+1/a = sqrt(16)=(+/-)4
Step-by-step explanation:
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