If a- b- c are rational numbers such that a2-b2-c2-a b-b c-c a-0- prove that a-b-c-

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Identities of Mathematical Operations

If a, b, c ar...

Question

If a, b, c are rational numbers such that a² + b² + c² − ab − bc − ca = 0, prove that a = b = c.

Open in App

Solution

Suggest Corrections

Similar questions

a, b

c

a^{2} + b^{2} + c^{2} - a b - b c - c a = 0

a = b = c

a^{2} + b^{2} + c^{2} - a b - b c - c a = 0

a = b = c

a + b + c = 0

\frac{a^{2}}{b c} + \frac{b^{2}}{c a} + \frac{c^{2}}{a b} =

\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}

a^{2} + b^{2} + c^{2} - a b - b c - c a = \frac{1}{2} [{(b - c)}^{2} + {(c - a)}^{2} + {(a - b)}^{2}]

Join BYJU'S Learning Program