Find the Value
\[ 9x^2 + 25y^2 = 181 \]
\[ xy = -6 \]
Find: \[ 3x + 5y \]
Solution:
Using identity:
\[ (a+b)^2 = a^2 + b^2 + 2ab \]
\[ (3x+5y)^2 = (3x)^2 + (5y)^2 + 2(3x)(5y) \]
\[ = 9x^2 + 25y^2 + 30xy \]
\[ = 181 + 30(-6) \]
\[ = 181 – 180 \]
\[ = 1 \]
\[ (3x+5y)^2 = 1 \]
\[ 3x+5y = \pm 1 \]