An algebra problem by A Former Brilliant Member

Algebra Level 1

If x = b − c , y = c − a , z = a − b x=b-c , y=c-a , z=a-b , then value of x 2 − y 2 + z 2 + 2 x z x^2-y^2+z^2+2xz is?

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A Former Brilliant Member by A Former Brilliant Member

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3 solutions

Edwin Gray
Jan 11, 2019

X^2 - y^2 + z^2 + 2xz = (x + z)^2 - y^2 = (b - c + a - b)^2 - (c a)^2 = (a - c)^2 - (c - a)^2 = a^2 - 2ac + c^2 - c^2 + 2ca - a^2 = 0. Ed Gray

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Marc Ballon
Nov 10, 2015

Factoring the question is equal to (x+y+z)(x-y+z). Substitute the values in x+y+z that is equal to 0.

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Akash Gupta
Nov 9, 2015

Substitute the values of x, y and z in the given expression. => (b-c)^2-(c-a)^2+(a-b)^2+2(b-c)(a-b). After expanding by the formula (a+b) the whole square=a square +b square +2 ab. It is seen that all the resulting terms cancel each other. So the result is 0.

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