Given that a, B and C are the three sides of the triangle ABC, and a square C square - b square C square = a 4 power - B power, try to judge the shape of the triangle ABC

Given that a, B and C are the three sides of the triangle ABC, and a square C square - b square C square = a 4 power - B power, try to judge the shape of the triangle ABC

There is a problem with the title. It should be that the shape of the triangle ABC is an isosceles triangle or a right triangle. The reason is that a? C? B? C? 2 = C? (a? B? 2) a ^ 4-b ^ 4 = (a? B? 2) (a? + B

It is known that a, B, C are the three sides of △ ABC, and a square C-B square C = the fourth power of A-B power to judge the shape of triangle

A square C-B square C = the fourth power of a-b-the fourth power of B a ^ 4-b ^ 4-A ^ 2C ^ 2 + B ^ 2C ^ 2 = 0 (a? + B?) (a? - B?) = 0 (a? - B?) (a? + B?) = 0, so a? - B? = 0 or a & sup

If a, B and C are the lengths of the three sides of △ ABC and satisfy A2 + 2B2 + c2-2b (a + C) = 0, then the shape of the triangle is______ .

From the known condition A2 + 2B2 + c2-2b (a + C) = 0, it is obtained that,
（a-b）2+（b-c）2=0
∴a-b=0，b-c=0
That is, a = B, B = C
∴a=b=c
So the answer is an equilateral triangle

Given that A.B.C is the three sides of the triangle ABC, and satisfies the square of a + the square of 2B + the square of C - 2b (a + C) = 0?

It's an equilateral triangle
a2 + b2 + b2 + c2 - 2ab - 2bc = 0
(a2 -2ab + b2) + (b2 - 2bc + c2) = 0
(a -b)2 +(b-c)2 =0
a=b b=c
a=b=c

If a, B and C are the lengths of the three sides of △ ABC and satisfy A2 + 2B2 + c2-2b (a + C) = 0, then the shape of the triangle is______ .

From the known condition A2 + 2B2 + c2-2b (a + C) = 0, it is obtained that,
（a-b）2+（b-c）2=0
∴a-b=0，b-c=0
That is, a = B, B = C
∴a=b=c
So the answer is an equilateral triangle

It is known that a, B, C are the three sides of the triangle ABC. If a, B, C satisfy the square of a + the square of C + 2B (b-a-c) = 0, judge the shape of the triangle

A^2+C^2+2B(B-A-C)=0
===>(A-B)^2+(C-B)^2=0
===>A=B=C
So it's an equilateral triangle

Given that the three sides a, B, C of the triangle ABC satisfy the equation A's square + C's Square - 2ab-2bc + 2B's Square = 0, try to judge the shape of triangle ABC How to do it

The square of a + the square of c-2ab-2bc + 2B = 0 (a-b) ^ 2 + (B-C) ^ 2 = 0 A-B = 0, B-C = 0, a = b = C triangle ABC is an equilateral triangle
Thank you!

It is known that a, B, C are the three sides of △ ABC and satisfy the relation A2 + C2 = 2Ab + 2bc-2b2. It is shown that △ ABC is an equilateral triangle

∵ the original formula can be changed into A2 + c2-2ab-2bc + 2B2 = 0,
a2+b2-2ab+c2-2bc+b2=0，
That is (a-b) 2 + (B-C) 2 = 0,
ν A-B = 0 and B-C = 0, that is, a = B and B = C,
∴a=b=c．
So △ ABC is an equilateral triangle

Given that the length of three sides a, B, C of triangle ABC satisfies the relation a ^ 2 + B ^ 2 = 2Ab = 2bc-2b ^ 2, try to explain that triangle ABC is an equilateral triangle As the title (1) Given that the length of three sides a, B, C of triangle ABC satisfies the relation a ^ 2 + C ^ 2 = 2Ab + 2bc-2b ^ 2, try to explain that triangle ABC is an equilateral triangle. (2) The three side lengths a, B, C of the triangle ABC satisfy the relation a ^ 2-C ^ 2 + 2ab-2bc = 0. Try to explain that the triangle ABC is an isosceles triangle.

(1) A ^ 2 + C ^ 2 = 2Ab + 2bc-2b ^ 2A ^ 2 + C ^ 2 + 2B ^ 2 + 2B ^ 2-2ab-2bc = 0 (a ^ 2-2ab + B ^ 2) + (b ^ 2-2bc + C ^ 2) = 0 (a-b) ^ 2 + (B-C) ^ 2 = 0A = B = C. Therefore, it is an equilateraltriangle (2) a ^ 2-C ^ 2 + 2ab-2bc = 0A ^ 2 + 2Ab + B ^ 2 = C ^ 2 + 2BC + B ^ 2 = C ^ 2 + 2BC + B ^ 2 (a + B + B ^ 2) (a + B + B ^ 2) (a + B + B ^ 2) ^ 2 = (B + C) ^ 2 = (B + C) ^ 2) ^ 2 = (B + C) ^ 2 = (2a + B = B + Ca = C

It is known that a, B, C are the three sides of △ ABC and satisfy the relation A2 + C2 = 2Ab + 2bc-2b2. It is shown that △ ABC is an equilateral triangle

∵ the original formula can be changed into A2 + c2-2ab-2bc + 2B2 = 0,
a2+b2-2ab+c2-2bc+b2=0，
That is (a-b) 2 + (B-C) 2 = 0,
ν A-B = 0 and B-C = 0, that is, a = B and B = C,
∴a=b=c．
So △ ABC is an equilateral triangle