Question

(x2 – x2 + xy - yz ) = ?​

Answer 1

Answer:

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1

azizkm786

31.05.2018

Math

Secondary School

+10 pts

Answered

Prove that x^2 +y^2 +z^2-xy-yz-zx is always positive.

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TheUrvashi

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hey

We have : x2 + y2 + z2 - xy - yz - zy

Now we multiply by in whole equation and get

2 ( x2 + y2 + z2 - xy - yz - zx )

⇒2 x2 + 2y2 + 2z2 - 2xy - 2yz - 2zx

⇒ x2 + x2 + y2 + y2 + z2 + z2 - 2xy - 2yz - 2zx

⇒ x2 + y2 - 2xy + y2 + z2 - 2yz + z2 + x2 - 2zx

⇒ ( x - y )2 + ( y - z )2 + ( z - x )2

From above equation we can see that for distinct value of x , y and z given equation is always positive .

Hope this information will clear your doubts about topic.

Answer 2

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