In order to do a good job in water conservancy construction, a village plans to build an 800m long channel with isosceles trapezoid cross section. (1) the design cross section area is 1.6m 2, the channel depth is 1m, and the width of the upper opening of the channel is 0.8m more than the width of the channel bottom, so the width of the upper opening and the channel bottom can be calculated. (2) a construction team undertakes the project and plans to complete it within the specified time. After four days of work, the equipment and the efficiency are improved The work efficiency is 10 meters more than the original plan. As a result, the task is completed 2 days ahead of the schedule

(1) Let the lower opening be x and the upper opening be x + 0.8, then x + X + 0.82 = 1.6 △ 1, and the solution is x = 1.2. After the test, x = 1.2 is the solution of the original equation. X + 0.8 = 2 A: the lower opening is 1.2 meters wide and the upper opening is 2 meters wide. (2) if we plan to dig x meters every day, then we can dig x + 10 meters every day after improving the efficiency

Given that a & # 178; + B & # 178; = 5, ab = 2, then (a + b) &# 178; =?

（a＋b）²＝a²＋b²+2ab=5+2*2=9

When a = √ 5 + 2, B = √ 5-2, the value of a & # 178; + AB + B & # 178; is
① When a = √ 5 + 2, B = √ 5-2, the value of a & # 178; + AB + B & # 178; is ()
② If a and B are rational numbers, and a + (√ 2) B = (3-2 √ 2) & # 178;, then a = (), B = ()

﹙1﹚a＋b＝√5＋2＋√5－2＝2√5
a·b＝√﹙√5＋2﹚﹙√5－2﹚＝1
∴ a²＋ab＋b²
＝﹙a＋b﹚²－ab
＝﹙2√5﹚²－1
＝19
﹙2﹚a＋√2·b＝﹙3－2√2﹚²＝17－12·√2
∴ a＝17
b＝﹣12.

(ab)²=?

(ab)²=a²b²
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Given x = 2 ＋ 5, y = 2 - √ 5, find the value of X & # 178; - Y & # 178

x＝2＋√5,y＝2－√5,
x^2-y^2=(x-y)(x+y)
=4*2*√5
=8√5

Given X & # 178; + Y & # 178; = 5, X-Y = 2, find the value of (x + y) &# 178
It's not difficult, but I'm not good at it. I'm looking for advice from experts

Given X & # 178; + Y & # 178; = 5, X-Y = 2, find the value of (x + y) &# 178; + Y & # 178; - 2XY = 4x & # 178; + Y & # 178; = 5, get 2XY = 5-4 = 1x & # 178; + Y & # 178; = 5, get X & # 178; + Y & # 178; + 2XY = 6 (x + y) &# 178; = 6

[mathematical calculation] the variances of 1,4,5,6,4 are (xy-x & # 178;) △ X & # 178; - 2XY + Y & # 178; / XY × X-Y / X & # 178;
The variance of 1,4,5,6,4 is ()
Simplified evaluation: (xy-x & # 178;) △ X & # 178; - 2XY + Y & # 178; / XY × X-Y / X & # 178;
x=8 y=1/3
The solution equation: X / X-2 - 1 = 2 / 4-x & # 178;

1、2.8
2、-x(x-y)×xy/(x-y)²×(x-y)/x²
=-y
When x = 8, y = 1 / 3
Original formula = - 1 / 3
3. Multiply both sides by (X-2) (x + 2)
x(x+2)-(x²-4)=-2
2x=-6
x=-3
Test: x = - 3 is the solution of the equation

The image of X & # 178; - 2x + 3 = y

Given that X and y are real numbers, x2y2 + x2 + 4xy + 13 = 6x, find the value of X and y

X2y2 + 4xy + 4 + x2-6x + 9 = 0, (XY + 2) 2 + (x-3) 2 = 0, ∵ (XY + 2) 2 ≥ 0, (x-3) 2 ≥ 0, ∵ XY + 2 = 0, x-3 = 0, ∵ xy = - 2, x = 3. Substituting x = 3 into xy = - 2, the solution is y = y = - 2 / 3

Given X & # 178; + 4Y & # 178; - 6x + 4Y + 10 = 0, find the value of 1 / x + 1 / y

x²+4y²-6x+4y+10=0
x²-6x+4y²+4y+10=0
x²-6x+9+4y²+4y+1=0
(x-3)²+(2y+1)²=0
x=3
y=-1/2
1 / x + 1 / Y
=1/x+1/y
=1/3+1/(-1/2)
=1/3-1/(1/2)
=1/3-2
=-5/3