Question

If x=7-4√3 then the value of x^3/2 + 1/x^3/2​

Answer 1

Answer:

52

Step-by-step explanation:

x = 7-4√3 = 4+3-4√3 = (2)²+(√3)²-2(2)(√3) = (2-√3)²

=> √x = x½ = √(2-√3)² = 2-√3 = y [ LET]

=> 1/y = 1/(2-√3)

= {1/(2-√3)}×{(2+√3)/(2+√3)}

= (2+√3)/(2+√3)(2-√3)

= (2+√3)/(2)²-(√3)²

= (2+√3)/(4-3)

= (2+√3)

=> y + 1/y = (2-√3) + (2+√3) = 2-√3+2+√3 = 4

=> x^3/2 + 1/x^3/2 = y³ + 1/y³ = (y + 1/y)³ - 3 × y × 1/y × (y + 1/y) = (y + 1/y)³ - 3(y + 1/y) = (4)³ - 3(4) = 64 - 12 = 52

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