Question

f(x)=x²-3x+1 and f(2a)=2f(a) find value of a

Answer 1

Answer:

$f(x) = {x}^{2} - 3x + 1 \\ \\ \\ f(2a) = 2f(a) \\ = > (2a) {}^{2} -6a + 1 = 2( {a}^{2} - 3a + 1 )\\ = > 4 {a }^{2} - 6a + 1 = 2 ({a}^{2} - 3a + 1) \\ = > 4 {a}^{2} - 6a + 1 = 2 {a}^{2} - 6a + 2 \\ = > 2 {a}^{2} = 1 \\ = > a = \frac{1}{ \sqrt{2} }$