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Please help me solve this maths problem. If k=8+60 ½ Then, k 1/2 +1/k 1/2 = ?????

Please help me solve this maths problem.
If k=8+60½  
Then, k1/2+1/k1/2 = ?????
 

Grade:8

1 Answers

Vikas TU
14149 Points
4 years ago
Let k1/2+1/k1/2 = a
squaring both sides we get,
k + 1/k + 2 = a^2
k + 1/k = a^2 – 2
put k value,
(8 + 60^(1/2))    +  1/(8+60^(1/2)) + 2 = a^2
(8 + 2root(15)) + 1/(8 + 2root(15)) + 2 = a^2
8 + 2root(15) + (8 – 2root15)/4 + 2 = a^2
a^2 = 10 + 2root15 + 2 – (root(15))/2
a^2  = 12 + 1.5*root(15)
a = root(12 + 1.5*root(15))
 

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