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问题: 数学

已知x+y=3-cos4Θ,x-y=4sin2Θ 求证x^1/2 + y^1/2=2.

解答:

已知x+y=3-cos4Θ,x-y=4sin2Θ 求证√x + √y = 2

x+y = 3-cos4θ = 2 + 2sin²2θ
x-y = 4sin2θ
--->x = 1+sin²2θ+2sin2θ = (1+sin2θ)²
  y = 1+sin²2θ-2sin2θ = (1-sin2θ)²
--->√x + √y = (1+sin2θ)+(1-sin2θ) = 2