Question

Prove that the value of
$x ^{2} + y {}^{2} + z {}^{2} + xy + yz + zx \:$
is 43 when x =4 , y = -6 and z = 5​​

Answer 1

Step-by-step explanation:

$x {}^{2} + y {}^{2} + z {}^{2} + xy + yz + zx \\ = (4) {}^{2} + ( - 6) {}^{2} + (5) {}^{2} + (4)( - 6) + ( - 6)(5) + (5)(4) \\ = 16 + 36 + 25 - 24 - 30 + 20 \\ = 77 - 54 + 20 \\ = 97 - 54 \\ = 43 \: \: (proved)$