if X=7+4√3 then find the value of x + 1/x
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Answer:
583-329√3
Step-by-step explanation:
x = 7+4√3
then
x+1/x = 7+4√3 + 1/7+4√3
= (7+4√3)^2+1 / 7+4√3
= {(7)^2+(4√3)^2+2(4√3) / 7+4√3
= 49 + 48 + 8√3 / 7+4√3
= 97+8√3 / 7+4√3
Rationalizing
= (97+8√3)(7-4√3) / (7+4√3)(7-4√3)
= (97+8√3)(7-4√3) / 49 - 48
= (97+8√3)(7-4√3) / 1
= (97×7)-(97×4√3)+(7×8√3)-(8√3×4√3)
= 679 -96 -388√3 +59√3
= 583 -329√3
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