Question

if 3a + 1/2a=6, find the value of 4a^2 + 1/9a^2​

Answer 1

Answer:

$3a + \frac{1}{2a} = 6 \\ 2a(3a + \frac{1}{2a} ) = 6 \times 2a \\ 6a + 1 = 12a \\ 12a - 6a = 1 \\ 6a = 1 \\ a = \frac{1}{6} \\ 4 {a}^{2} + \frac{1}{9a ^2} = 4 \times (\frac{1}{6})^{2} + \frac{1}{9( \frac{1}{6}) ^{2} } \\ = 4 \times \frac{1}{36} + \frac{1}{9( \frac{1}{36 }) } \\ = \frac{1}{9} + 4 \\ = \frac{1 + 36}{9} \\ = \frac{37}{9}$