√x2/x1 + √x1/x2 =怎么推导 用韦达定理推设一元二次方程2x²+7x+1=0两个根x1 x2,不解方程求值x2/x1+x1/x2|x1-x2|√(x2/x1) + √(x1/x2)

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√x2/x1+√x1/x2=怎么推导用韦达定理推设一元二次方程2x²+7x+1=0两个根x1x2,不解方程求值x2/x1+x1/x2|x1-x2|√(x2/x1)+√(x1/x2)√x2/x

√x2/x1 + √x1/x2 =怎么推导 用韦达定理推设一元二次方程2x²+7x+1=0两个根x1 x2,不解方程求值x2/x1+x1/x2|x1-x2|√(x2/x1) + √(x1/x2)
√x2/x1 + √x1/x2 =怎么推导 用韦达定理推
设一元二次方程2x²+7x+1=0两个根x1 x2,不解方程求值
x2/x1+x1/x2
|x1-x2|
√(x2/x1) + √(x1/x2)

√x2/x1 + √x1/x2 =怎么推导 用韦达定理推设一元二次方程2x²+7x+1=0两个根x1 x2,不解方程求值x2/x1+x1/x2|x1-x2|√(x2/x1) + √(x1/x2)
显然有:
x1x2=1/2,x1+x2=-7/2.
①x2/x1+x1/x2
=(x1^2+x2^2)/(x1x2)
=[(x1+x2)^2-2x1x2]/(x1x2)
=(49/4-2×1/2)/(1/2)
=45/2.
②|x1-x2|
=√[(x1+x2)^2-4x1x2]
=√(49/4-4×1/2)
=√41/2.
③√(x2/x1)+√(x1/x2)
=(x1+x2)/√(x1x2)
=(-7/2)/√(1/2)
=(-7√2)/2.