Question

If 2a = 3b, find the value of 4a^2-12ab+9b^2

Answer 1

$\huge\underline {\green{\sf {Answer:}}}$

$\underline {\bold{\pink{Given:}}}$

➣$2a = 3b$

$\underline {\bold {Find:}}$

➣$4a^2 - 12ab + 9b^2$

$\underline {\bold {\pink{Solution:}}}$

✮Taking the given relation :

➫$2a = 3b$

➫$2a - 3b = 0$⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$-(i)$

✮Now :

➫$4a^2 - 12ab + 9b^2$

➫$(2a)^2 - 2 \times 2a \times 3b + (3b)^2$

➫$(2a - 3b)^2$

✮Putting value of $2a - 3b$ from $(i)$:

➫$(0)^2$

$\boxed{\implies{\boxed{4a^2 -12ab +9b^2 = 0}}}$

Answer 2

Answer:

$\large\boxed {4a^2-12ab+9b^2=0}$

Step-by-step explanation:

Given:-

2a=3b

To Find:-

4a²-12ab+9b²= ?

Formula Applied:-

(a-b)²=a²-2ab+b²

Solution:-

 4a²-12ab+9b²

⇒(2a)²-2(2a)(3b)+(3b)²

⇒(2a-3b)²                     [∵(a-b)²=a²-2ab+b²]

⇒(3b-3b)²                     [∵2a=3b]

⇒(0)²

⇒0

∴ The Value of $\large\boxed {4a^2-12ab+9b^2=0}$.