Question

If 2x – y + z = 0, prove that 4x² - y² +z²+ 4xz = 0​

Answer 1

Step-by-step explanation:

4x² + y² + z² -4xy -2yz +4xz = 0

(2x)² + y² + z² +2(2x)(-y)+2(-y)z +2(2x)z =0

use formula,

(a + b + c)² = a² + b² + c² +2(ab+bc+ca)

now,

(2x -y + z)² = 4x² +y² +z² -4xy -2yz +4xz =0

so, (2x -y -z)² is factor of given

Answer 2

Step-by-step explanation:

To prove 4x² - y² + z² + 4xy = 0

Here,

2x - y + z = 0

Therefore, (2x - y + z) is a factor.

(2x - y + z)² is also a factor

(2x - y + z)²

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

[ ,

(++) = (²+²+²+2+2+2)

=²+²+²+ 2(++)]

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

= 4x² + y² + z² - 4xy - 2xy + 4xy

Hence proved!!

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