Question

已知a=1/2+根号3,b=1/2-根号3,则根号(a平方+b平方-4)=

请写清楚答题过程

Answer 1

a = 1/2 + √3
b = 1/2 - √3

则:
√(a² + b² - 4)
= √(a² + b² + 2ab - 2ab - 4)
= √{ (a+b)² - 2ab - 4}
= √{ (1/2 + √3 + 1/2 - √3)² - 2(1/2 + √3)(1/2 - √3) - 4}
= √{ (1/2 + 1/2 )² - 2[(1/2)² - (√3)²] - 4}
= √{ (1 )² - 2[ 1/4 - 3 ] - 4}
= √{ 1 - 2/4 + 6 - 4}
= √(3 - 1/2)
= √(5/2)
= √10 / 2

Answer 2

a² + b² =(a+b)²-2ab=1- 2(1/2 + √3)(1/2 - √3)=1-2(1/4-3)=13/2
a² + b² -4=5/2
√(a² + b² - 4)=√(5/2)= √10 / 2