Question

Please answer my question please please
If X+y+z=7 and xy+yz+zx=6 find x^2+y^2+z^2

Answer 1

$Given \: \: Question \: \: Is \: \\ \\ x + y + z = 7 \: \: \: \: \: xy + yz + zx = 6 \\ \\ find \: \: \: x {}^{2} + y { }^{2} + z {}^{2} \\ \\ Answer \: \\ \\ x + y + z = 7 \\ \\ Squaring \: \: on \: both \: sides \: we \: have \\ \\ (x + y + z) {}^{2} = 7 {}^{2} \\ \\ x {}^{2} + y {}^{2} + z {}^{2} + 2xy + 2yz + 2zx = 49 \\ \\ x {}^{2} + y {}^{2} + z {}^{2} + 2(xy + yz + zx) = 49 \\ \\ x {}^{2} + y {}^{2} + z {}^{2} + 2(6) = 49 \\ \\ x {}^{2} + y {}^{2} + z {}^{2} + 12 = 49 \\ \\ x {}^{2} + y {}^{2} + z {}^{2} = 49 - 12 \\ \\ x {}^{2} + y {}^{2} + z {}^{2} = 37 \\ \\ Therefore \: \: \: \: x {}^{2} + y {}^{2} + z {}^{2} = 37 \\ \\ Note \\ \\ \: (a + b + + c) {}^{2} = a {}^{2} + b {}^{2} + c {}^{2} + 2ab + 2bc + 2ac$

Answer 2

Answer:

Step-by-step explanation:

x+y+z =7

x+yz+zx=6

Now,

(x+y+z)^2 = x^2+y^2+z^2 +2xy+2yz+2zx

since x+y+x =7

Hence

(7)^2 =x^2+y^2+z^2 + 2(xy+yz+zx)

49 = x^2+y^2+z^2 + 2 × 6

Or x^2+y^2+z^2 =49 - 12 =37

Hope it is clear. Pls mark as brainliest