If 2x-3y - 3y-4z- show that - 4x2 - 9y2 - 16z2 - 2x - 3y - 4z 2x - 3y - 4z

2x/3y = 3y/4z = gt;8xz/3yz=1 = gt;8xz=9y^2 —— nbsp;(i)L.H.S =4x^2+9y^2+16z^2 nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; ...

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(a-b)^2 Expansion and Visualisation

If 2x/3y = ...

Question

If $\frac{2 x}{3 y} = \frac{3 y}{4 z}$ , show that :
$4 x^{2} + 9 y^{2} + 16 z^{2} = (2 x - 3 y + 4 z) (2 x + 3 y + 4 z)$

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Solution

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\frac{2 x}{3 y} = \frac{3 y}{4 z}

4 x^{2} + 9 y^{2} + 16 z^{2} = (2 x - 3 y + 4 z) (2 x + 3 y + 4 z)

4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y - 24 y z - 16 x z

= (2 x + 3 y - 4 z) (2 x + 3 y - 4 z)

{(2 x - 3 y)}^{3} + {(4 z - 2 x)}^{3} + {(3 y - 4 z)}^{3}

2 x + 3 y + 4 z = 7

2 x + 3 y + 4 z = 17

(4 x^{2} + 9 y^{2}

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