Find the Value
\[ 3x – 7y = 10 \]
\[ xy = -1 \]
Find: \[ 9x^2 + 49y^2 \]
Solution:
Using identity:
\[ (a-b)^2 = a^2 + b^2 – 2ab \]
\[ (3x-7y)^2 = (3x)^2 + (7y)^2 – 2(3x)(7y) \]
\[ = 9x^2 + 49y^2 – 42xy \]
\[ = (10)^2 \]
\[ 100 = 9x^2 + 49y^2 – 42(-1) \]
\[ 100 = 9x^2 + 49y^2 + 42 \]
\[ 9x^2 + 49y^2 = 100 – 42 \]
\[ = 58 \]