A 2 b 2 c 2 ab bc ca 0

Asked by admin @ 02/08/2021 in Math viewed by 288 People

A^2+b^2+c^2-ab-bc-ca =0 then prove that a=b=c

Answered by admin @ 02/08/2021

Consider, a2 + b2 + c2 – ab – bc – ca = 0

Multiply both sides with 2, we get

=>2( a2 + b2 + c2 – ab – bc – ca) = 0

=> 2a2 + 2b2 + 2c2 – 2ab – 2bc – 2ca = 0

=> (a2 – 2ab + b2) + (b2 – 2bc + c2) + (c2 – 2ca + a2) = 0

=> (a –b)2 + (b – c)2 + (c – a)2 = 0

Since the sum of square is zero then each term should be zero

=> (a –b)2 = 0, (b – c)2 = 0, (c – a)2 = 0

=> (a –b) = 0, (b – c) = 0, (c – a) = 0

=> a = b, b = c, c = a

∴ a = b = c

HOPE U UNDERSTAND

PLS MARK IT AS BRAINLIEST

The lengths of the sides of a right triangle are a and b, and the hypotenuse is c. find the area of the triangle. b = 2 in.; c = 6 in. a = sq. in.

Asked by maham237 @ 13/01/2021 in Mathematics viewed by 327 persons

A 2 b 2 c 2 ab bc ca 0

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