Find the Value
\[ 2x + 3y = 8 \]
\[ xy = 2 \]
Find: \[ 4x^2 + 9y^2 \]
Solution:
Using identity:
\[ (a+b)^2 = a^2 + b^2 + 2ab \]
\[ (2x+3y)^2 = (2x)^2 + (3y)^2 + 2(2x)(3y) \]
\[ = 4x^2 + 9y^2 + 12xy \]
\[ = (8)^2 \]
\[ 64 = 4x^2 + 9y^2 + 12(2) \]
\[ 64 = 4x^2 + 9y^2 + 24 \]
\[ 4x^2 + 9y^2 = 64 – 24 \]
\[ = 40 \]