Question

plz someone help me to do this no.​

Answer 1

Given:

3x - y + z =0

To prove:

9x² - y² + z² + 6xz = 0

Solution:

3x - y + z = 0

3x + z = -y

(3x + z)² = (-y)²

9x² + z² + 2.3x.z = y²

9x² + z² - y² + 6xz = 0

Hence Proved

Answer 2

Given

$\mathtt{3x - y + z = 0}$

To prove

$\mathtt{9 {x}^{2} + {z}^{2} - {y}^{2} + 6x z } = 0$

Proof

$\mathtt{as \: given} \\ \\ \mathtt{3x - y + z = 0} \\ \\ \mathtt{3x + z = y} \\ \\ \mathtt{squaring \: both \: sides} \\ \\ \mathtt{ {(3x + z)}^{2} = {y}^{2} } \\ \\ \mathtt{9 {x}^{2} + {z}^{2} + 6xz = {y}^{2} } \\ \\ \mathtt{9 {x}^{2} + {z}^{2} - {y}^{2} + 6xz = 0 }$

$\mathtt{\pink{hence \: proved}}$