HELP!!! Grade 11 math question!?

Question

If x + y + z = 1 and x^2 + y^2 + z^2 = 3

what is the value of xy + xz + yx?

The answer at the back of the textbook says "-1" (they sometimes make mistakes) but I need to know HOW to get the answer, not what the answer is.

Please help! I'm stuck!!!

Answer 1

in the first equation, find z in terms of x and y, and plug this into the second equation I believe, then eh I don't know, sorry, can't help ya with your algebra 2, had that last year. Hated algebra 2. That was the worst math class I ever had.

Answer 2

x+x*2+y+y*2+z+z*2=1+3

x+(x)*2+y+(y)*2+z+(z)*2=4

x+y+z+(x+y+z)*2=4

haha this is the best I can do...haven't done algebra in a million years...

can you give me the formula your text book offers?

Answer 3

We have x + y + z = 1

therefore (x + y + z)^2 = 1

expanding it we have x^2 + y^2 +z^2 + 2xy + 2yz + 2xz =1

plugging in the value of x^2 + y^2 + z^2 = 3, we have:

2xy + 2yz + 2xz + 3 = 1

therefore xy +yz + xz = -1

Answer 4

x= 1

y=1

z=-1



This way 1+1+(-1) = 1

and   1^2 + 1^2 + (-1)^2 = 3

So 1x1 + 1x-1 + 1x-1 = -1

Answer 5

X = 1, Y = -1, Z = 1  PLUG 'N CHUG

1 + (-1) + 1 = 1

1² + (-1)² + 1² = 1 + 1 + 1 = 3

(1*-1) + (1*1) + (-1*1) = (-1) + 1 +(-1) = -1

BAM