Question

Solve log, X^2- 5X + 14 = 3.​

Answer 1

$Given \:log _{10} \:(x^{2}-5x+14) = 3$

$\implies x^{2}-5x+14 = 10^{3}$

$\implies x^{2}-5x+14 = 1000$

$\implies x^{2}-5x+14 - 1000 = 0$

$\implies x^{2}-5x -986 = 0$

/* Splitting the middle term, we get */

$\implies x^{2}-34x + 29x - 986 = 0$

$\implies x( x - 34 ) + 29( x - 34 ) = 0$

$\implies (x-34)(x+29) = 0$

$\implies x-34 = 0 \:Or \: x+29 = 0$

$\implies x = 34 \:Or \: x = - 29$

Therefore.,

$\green { x = 34 \:Or \: x = - 29}$

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