A triangle with a b , 2ab, a b a b 0 with side lengths is triangle why? ）

The first thing to consider is the special triangle. Because (a b 0), it can be determined that a +b is the largest edge, i.e., the hypotenuse. Therefore, it can be predicted that the sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse.

The sum of squares of two right-angled sides:

a2 -b2 ）2 +（2ab）2 =a4 -2a2b2 +b4 +4a2b2 =a4 +2a2b2 +b4 =（a2 +b2 ）2

The square of the hypotenuse: (a2 +b2)2

That is, the sum of the squares of the two right-angled edges is equal to the square of the hypotenuse. Therefore, the triangle is determined to be a right triangle.

Right-angled triangle.

A + B) = (A - B) + (2AB) Squared.

（a²+b²）²=(a²)²2a²b²+(b²)²a²)²2a²b²+(b²)²4a²b²(a²-b²)²2ab)²

From the Pythagorean theorem, it can be seen that the triangle on these three sides is a right triangle.

2ab)^2+(a^2-b^2)^2=(a^2+b^2)^2

So it's a right-angled triangle.

a^2-2ab+b^2+b^2-2bc+c^2=0a-b)^2+(b-c)^2=0

The town is dressed up.

a-b=0a=b

b-c=0b=c

Therefore, the a=b=c triangle is an equal stove side triangle.

Multiply 2 by 2 on both sides at the same time to obtain: 2a 2+2b 2+2c 2-2ab-2bc-2ac=0

Split into full squares of the lift and drain.

a-b) 2+(b-c) 2+(a-c) 2=0 The perfect square must be greater than or equal to the smile of the pants and there is no zero, so a=b,b=c,a=c, i.e. a=b=cEquilateral triangular Huna shape.

Answer: It is an equilateral reed.

Proof : Multiply both sides of the equation by 2 to get:

A 2ab b a 2ac c b 2bc c =0, a b a c b c = 0, by the sum of three non-negative numbers = 0, then each number hits the jujube belt = 0, a = b, a = c, rock mill b = c, a = b = c, is equilateral .

(a²-b²)²2ab)²

A to the 4th power - 2a b + b to the 4th power + 4a b = a to the 4th power + 2a b + b to the 4th power.

a²+b²)²

A triangle is a right-angled triangle.

Answer: (a 2+b 2) 2=a 4+2a 2b 2+b 4(a 2-b 2) 2=a 4-2a 2b 2+b 4(2ab) 2=4a 2b 2

So: (A 2-B 2) 2+(2AB) 2=(A 2+B 2) 2 So: The triangle ABC is a right triangle and the hypotenuse is A 2+B 2

Right-angled triangle. Because (a -b ) 2ab) = (a +b ) then a +b is the hypotenuse, a -b and 2ab are two right-angled edges.

Right-angled triangle.

The difference between the first two squares is equal to the square of the third term.

Right triangle because.

a²-b²)^2+(2ab)^2

a^4+b^4-2a^2b^2+4a^2b^2=a^4+b^4+2a^2b^2

a^2+b^2)^2

Satisfy the Pythagorean law.

Let a, b, and c be the three sides of a triangle and have: a=a-b, b=2ab, c=a+b

It yields: a = (a -b) = (a) 2a b + (b) b =(2ab) =4a b

c²=(a²+b²)²

a²+b²=(a²)²2a²b²+(b²)+4a²b²=(a²)²2a²b²+(b²)²

a²+b²)²

That is: a +b = c satisfies the Pythagorean theorem.

So the triangle is a right triangle.

(a-b)(a²+b²-c²）=0

a-b=0 or a+b-c=0

So a = b or a + b = c

So it's an isosceles triangle or a right triangle.

Satisfying the relation = 0, i.e., either a=b, a2+b 2=c 2, or both, is required. So the triangle can be an isosceles triangle, or a right triangle.

(a-b)(a²+b²-c²）=0

a-b=0 or a +b -c =0 or both equals 0 at the same time, so a=b or a +b =c or (a=b and a +b =c) so it is an isosceles triangle or a right triangle or an isosceles right triangle.

The title is a triangle that satisfies a-b=0 or a+b-c=0.

The former satisfies the isosceles triangle, the latter satisfies the right triangle, and both satisfy the isosceles right triangle.

Because (a-b)(a+b-c)=0

So, a-b=0 or a+b-c =0, (1)a-b=0, i.e., a=b, so isosceles triangle (2)a+b-c =0, i.e., a+b =c, so it's a right triangle.

(a²-b²)²2ab)²

a^4-2a²b²+b^4+4a²b²

a^4+2a²b²+b^4

a²+b²)²

A triangle with a +b, a -b, and 2ab on three sides is a right-angled triangle.

(a²-b²)+2ab）²

a^4+b^4-2a²b²+4a²b²

a^4+b^4+2a²b²

a²+b²）²

So it's a right triangle.

Solution: The left factor is factored to obtain a 2(b-c)+b 2(b-c)=0; (b-c)(a^2+b^2)=0;Because a2+b2 0, b-c=0;So the triangle is an isosceles triangle.

a²+b²+c²-ab-ac-bc=0

2 (sell hall a +b +c -ab-ac-bc) = 0a +b -2ab + a +c -2ac -2bc + b +c =0a-b) +a-c) +b-c) middle hand hidden = 0 so a = b = c equilateral triangular potato plum shape.

Solution: The equation a +b +c Lu 晌infiltrat-ab-ac-bc=0 is multiplied by 2 at the same time.

2a +2b +2c -2ab-2ac-2bc=0a early ridge + a + b + b + c + c -2ab-2ac-2bc = 0

a-b) 2+(b-c) 2+(c-a) 2=0, so return a=b=c