if x=7+4√3 find the value of √x+1/√x
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Answer:
x = 7+4√3
To find √x we proceed,
√x = √(7+4√3)
√x = √(7+2x2√3)
√x = √(7+2√3x4)
√x = √(3+4+2√3x4)….. {writing 7 = 3+4}
If we observe RHS of √x we observe form of
√(a² + b² +2ab) where a=√3 and b =√4
Hence, √x =√(√3 +√4)² = √3 + √4 = 2+√3
√x = 2+√3
1/√x = 1/(2+√3)
Multiplying both numerator and denominator by 2 - √3, we get
1/√x = (2-√3)/(2-√3)(2+√3) = (2-√3)/(2²-√3²) =
1/√x = 2-√3
Hence √x +1/√x = 2+√3 +2 -√3 = 4
Step-by-step explanation:
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Step-by-step explanation:
x = 7 - 4√(3) then find value of (i) (√(x) + 1√(x)) (ii) (√(x)- 1√(x))
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