Question

If x2 + 4y2 + 9z2 – 6yz - 3zx - 2xy = 0, then

please say this qnswer​

Answer 1

ANSWER

x

2

+4y

2

+9z

2

−6yz−3zx−2xy

=

2

1

((x−2y)

2

+(2y−3z)

2

+(3z−x)

2

)

This is the sum of 3 squares. So this term is greater than or equal to 0.

Equality occurs when, x=2y, 2y=3z, 3z=x

Answered By

Answer 2

Step-by-step explanation:

x²+(2y)²+(3z)² - 2xy - 6yz -3zx = 0

multiply by 2 on both sides

2x² + 2(2y)² +2(3z)² - 2(2xy) - 2(6yz)-2(3zx) = 0

x² -2*x*2y +(2y)² +

(2y)² -2*2y*3z+(3z)² +

(3z)² -2*3z*x + x² =0

(x-2y)² +

(2y - 3z)² +

(3z - x)² =0

sum of 3 squares is zero implies each term is zero

= x-2y=0

2y-3z=0

3z-x=0

x=2y =3z