If x=2+√3 find the value of …
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Posted by Aditya Raj 4 years, 4 months ago
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Yogita Ingle 4 years, 4 months ago
x+1/x =2+√3+1/2+√3
=[2+√3][2+√3]+1/2+√3 [taking LCM ]
=[2+√3]2+1/2+√3
=4+3+[4×√3]+1/2+√3
=8+4√3/2+√3
=[8+4√3/2+√3]×[2-√3/2-√3] [by rationalising the denominator]
=[8+4√3][2-√3]/[2]2-[√3]2
=16-8√3+8√3-4[√3]2
=16-12
x+1/x=4
[x+1/x]3=43 [cubing both side]
x3+1/x3+3×x×1/x[x+1/x]=64 [using {x+y}3]
x3+1/x3+3×4=64 [substituting the value of x+1/x]\
x3+1/x3=64-12
x3+1/x3=52
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