If $f (x) = x^{2} - 3 x + 4$ , then find the value of 3( $x_{1} + x_{2}$ ) if $x_{1}, x_{2}$ satisfying $f (x) = f (2 x + 1) .$

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Solution

$f (x) = f (2 x + 1) x^{2} - 3 x + 4 = (2 x + 1)^{2} - 3 (2 x + 1) + 4 x^{2} - 3 x = 4 x^{2} + 4 x + 1 - 6 x - 3 3 x^{2} + 2 x - 2 = 0 i f r o o t s a r e x_{1}, x_{2}, t h e n 3 (x_{1} + x_{2}) = 3 \times (\frac{- 2}{3}) = - 2$

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