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As shown in the figure, in equilateral △ ABC, point D is the midpoint of BC side, and ad is taken as the edge to make equilateral △ ade. (1) find the degree of ∠ CAE; (2) take the midpoint F of AB side, connect CF and CE, and try to prove that quadrilateral afce is rectangular
（1） ∵△ ABC is an equilateral triangle, and D is the midpoint of BC, which is bisected by ∵ Da, that is, ∵ △ DAE is an equilateral triangle, and ∵ DAE = 60 °; ∵ CAE = ∵ Dae - ∵ CAD = 30 °; (2) it is proved that ∵ △ BAC is an equilateral triangle, f is the midpoint of AB, and ≁ CF ⊥ AB; ∵ BFC = 90 ° from (1) we know that ∵ CAE = 30 ° and ∵ BAC = 60 °; ∵ FAE = 90 °, AE ∥ CF; ∵ BAC is an equilateral triangle In this paper, we introduce a triangle with two sides, and AD and CF are the middle lines of BC and ab sides respectively, ∧ ad = CF; ad = AE, ∧ CF = AE; ∧ quadrilateral afce is a parallelogram; ∧ AFC = ∧ FAE = 90 ° and ∧ quadrilateral afce is a rectangle
Define a new operation: for any real number a and B, there is a ⊕ B = a (a-b) + 1. On the right side of the equation are the usual addition, subtraction and multiplication operations, such as: 2 ⊕ 5 = 2 × (2-5) + 1 = 2 × (- 3) + 1 = - 6 + 1 = - 5. If 2x ⊕ (1-x) = 5, find the value of X
2x♁(1-x)=5,
Namely
2x*[2x-(1-x)]+1=5
2x*(3x-1)+1=5
3x^2-x-2=0
The solution is x = 1 or x = - 2 / 3
What is the difference between real number and imaginary number? What is the meaning of imaginary number?
Give a definite definition
Real numbers include rational numbers (numbers that can be written as fractions, such as 2 / 3,2 / 1) and irrational numbers (numbers that cannot be written as fractions, infinite non cyclic decimals). Rational numbers include integers and the simplest fraction. The general formula of imaginary numbers is: C = a + bi, a and B are real numbers. If B = 0, then C is real number; if a = 0, then C is pure imaginary number. In complex space coordinates, real numbers are x-axis, The imaginary unit I is the y-axis unit,
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