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Root number B - root number A +8 > A - root number ab + "root number B B - root number ab - root number a a + root number ab> divided by 8 root number ab root number a + root number b = ( b - a + 8) a ( a - b) + [ 8 ( b - a) - 8 ( a + b)]*a+ b) 8 ab = ( b - a + 8) a ( a - b) + 8 a ( b- a ( b- a) (
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a 2 + b 2-c 2) 2-4a 2b 2 flat match chaotic variance.
a 2+2ab+b 2-c 2)(a 2-2ab+b 2-c 2)[(a+b) 2-c 2][(a-b) 2-c 2](a+b+c)(a+b-c)(a-b+c)(a-b-c) The sum of the two sides of the triangle is greater than the first argument and the three carrying sides.
So a+b-c>0
a-b+c>0
a-b-c0
Three positive and one negative, multiplied less than.
So(a2+b2-c2) 2-4a2b2
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Suppose a>b compares (a 2-ab+b 2) and a, i.e., their square comparison a 2-ab+b 2-a 2=b(b-a)< 0 compares (a 2-ab+b 2) and b, i.e., their square comparison a 2-ab+b 2-b 2=a(a-b)>0 so a> (a 2-ab+b 2)>b according to the cosine theorem cosq= [a 2+b 2-(a 2-ab+b 2)] (2ab)=1 2 q = 60 degrees.
If a
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cosc=(a2+b2-c2) 2ab=-1 2,c=120 degrees, which is the maximum angle, because there cannot be two inside angles greater than 90 degrees within a triangle.
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> = 0m is greater than or equal to zero.
a-b)²-c²
a-b+c)(a-b-c)
a+c>b a-b+c>0
b+c>a a-b-c<0
m-c²<0
m-c is less than zero.
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m 0 because m = (a-b)2
When a=b, the original = 0
When a=b, the original = 0
m-c is less than zero.
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(a 2+b 2-c 2) 2-4a 2b 2 (factorization) = (a 2 + b 2-c 2 + 2ab) (a 2 + b 2-c 2-2ab).
(a+b) 2-c 2][(a-b) 2-c 2] (refactoring).
a+b+c)(a+b-c)(a-b+c)(a-b-c) Since the sum of any two sides of the triangle is greater than the third side, the first three formulas in the above equation are all greater than 0, and only the last equation is less than 0, so [a +b -c] 4a b must be a negative value.
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by the previous step. a-c=2b(a-c)
Move the number to the right of the equal sign to the left.
Amount. a-c)+2b(a-c)=0
The common factor (a-c) is then extracted
And I got it. a-c)(1+2b)=0
Sorted out. a-c)(2b+1)=0
This step is just a variation of the equation. Hope.
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Because a-c = -2b (a-c).
So (a-c) + 2b (a-c) = 0 (move the number to the right of the equal sign to the left) (property of equation 1).
So (a-c) (1 + 2b) = 0 (extract the common factor (a-c)) so (a-c) (2b + 1) = 0
Actually, this step is just a variation of the equation. ^_
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Move the right side of the equation to the left, and then mention the common a-c
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1) If a, b, and qi ji c are the three high chain balance sides of the triangle, verify that a 2-2ab- c 2+b 2b, a-b+c>0
b+c>a,a-b-c
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Solution: 3c=12, c=4, a+b=8 , a-b=2 from the first two formulas, and a=5 and -b=3 from +
a=5,b=3,c=4
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Because a plus b plus c = 12, and a plus b = 2c, a-b = 2, a = 5, b = 3, c = 4
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Triangle area formula.
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When the sum of the three sides of the triangle is greater than the third side, the triangle is obtuse and acute. When the sum of the three sides of a triangle satisfies the sum of the squares of the two right-angled sides equals the square of the third side, the triangle is a right-angled triangle.