Question

一道高一的数学题……化简√5-2√6+√5+2√6

√5-2√6+√5+2√6
5-2√6在根号里
5+2√6在根号里
化简

Answer 1

你好！

设a = √(5－2√6) ，b = √(5+2√6)
则 a² + b² = (5－2√6)+(5+2√6) = 10
ab = √ [(5－2√6)(5+2√6) ] = √[5²－(2√6)²] = 1
(a+b)² = a²+b²+2ab = 12
∵a>0，b>0

∴a+b = √12 = 2√3

Answer 2

√(5-2√6)+√(5+2√6)

=√(10-4√6)/2+√(10+4√6)/2
=√(√6-2)²/2+√(√6+2)²/2
=(√6-2)/√2+(√6+2)/√2
=2√6/√2
=2√3

Answer 3

√(5-2√6)+√(5+2√6)
=√(√3-√2)²+√(√3+√2)²
=√3-√2+√3+√2
=2√3

Answer 4

设x=5-2√6 y= 5+2√6
有x^2+y^2=10 x*y=25-24=1
所以原式=x+y=√(x^2+y^2)+2x*y=√12=2√3

Answer 5

前面的根号里面的是根号三减根号2的平方，后面是根号三加根号2的平方，最后结果是2个根号三