Master Li bought back a rectangular sheet of iron from the market. After cutting off a square with a side length of 1 meter from each corner of the rectangular sheet, the rest of the box was just enclosed into a 6 cubic meter uncovered rectangular transport box. The bottom of the box was 1 meter longer than the width. It is known that it costs 20 yuan per cubic meter to buy this sheet of iron. How much did Master Li spend on buying this rectangular sheet of iron?

Master Li bought back a rectangular sheet of iron from the market. After cutting off a square with a side length of 1 meter from each corner of the rectangular sheet, the rest of the box was just enclosed into a 6 cubic meter uncovered rectangular transport box. The bottom of the box was 1 meter longer than the width. It is known that it costs 20 yuan per cubic meter to buy this sheet of iron. How much did Master Li spend on buying this rectangular sheet of iron?

Let the rectangle be x in length and Y in width. He cuts off the four corners of the rectangular sheet iron with a square with a side length of 1m. Then the part under the bottom area of (X-2) (Y-2) just encloses a 6 cubic meter uncovered rectangular transport box 1 * (X-2) (Y-2) = 6, and the bottom surface of the rectangular transport box is 1 meter longer than the width (X-2) - (Y -

 
 
In RT △ ABC, ab = AC, ∠ a = 90 °, D is any point on the edge of BC, de ⊥ AB is at point E, f is a point on AC, and AF = ed, M is the midpoint of BC. Try to judge what shape of triangle △ MEF is, and prove your conclusion

Reason: △ MEF is an isosceles right triangle. Reason: it connects am. Because △ ABC is RT △ and ∠ a = 90 ° AB = AC, so ∠ B = ∠ C = 45 ° am ⊥ BC, BM = cm = am, am bisects ∠ BAC, that is, ∠ cam = ∠ B = 45 ° and AF = ed = be, so △ BFM ≌ △ AEM. So FM = em, ∠ BME = ∠ AMF, because ∠ BME + ∠ ame = 90 °, so ∠ ame + ∠ AMF = ∠ EMF = 90 °, so △ MEF is an isosceles right triangle

1. Given ABC = 1, the solution of the equation x / (1 + A + AB) + X / (1 + B + BC) + X / (1 + C + Ca) = 2004 is______ .
There is a mistake in the previous topic, please ask again
2. Let m, n satisfy m < n, and 1 / (M2 + m) + 1 / [(M + 1) 2 + (M + 1)] + +1 / (N2 + n) = 1 / 23, then the value of M + n is______ .

Known ABC = 1
A / (AB + A + 1) = A / (AB + A + ABC) = 1 / (BC + B + 1)
C / (Ca + C + 1) = C / (Ca + C + ABC) = 1 / (a + 1 + AB)
A = 1 / BC can be obtained from ABC = 1, and BC / (BC + B + 1) can be obtained by substituting it into 1 / (a + 1 + AB)
So:
a/（ab+a+1）+b/（bc+b+1）+c/（ca+c+1）=（bc+b+1）/（bc+b+1）=1
So the solution of the original equation is x = 2004
1/(n^2+n)=1/n(n+1)=(n+1-n)/n(n+1)=(n+1)/n(n+1)-n/n(n+1)=1/n-1/(n+1)
So 1 / (M2 + m) + 1 / [(M + 1) 2 + (M + 1)] + +1/(n2+n)
=1/m-1/(m+1)+1/(m+1)-1/(m+2)+...+1/n-1/(n+1)
=1/m-1/(n+1)
It is known that its value is 1 / 23, so it can be concluded that
1/m-1/(n+1)=（n+1-m)/m(n+1)=1/23=(23-1)/23*22
Because the positive integer m, n satisfies m < n
M = 22, N + 1 = 23 * 22 = 506, n = 505
M + n = 527