Question

solve
(3x+8 / 2x + 3 ) - 5 √ ( 3x + 8 / 2x + 3 ) + 6 = 0

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Answer 1

Step-by-step explanation:

We have,

$\frac{3x + 8}{2x + 3} - 5 \sqrt{ \frac{3x + 8}{2x +3 } } + 6 = 0$

$Let\:\: \sqrt{\frac{3x+8}{2x+3}}=y$

So, the given expression becomes,

${y}^{2} - 5 y+ 6 = 0$

$\implies{y}^{2} - 3 y - 2y+ 6 = 0$

$\implies \: y( y - 3)- 2(y - 3) = 0$

$\implies \:( y - 2)( y - 3) = 0$

$\implies \: y = 2 \: \: or \: \: y = 3$

$\implies \: \sqrt{ \frac{3x + 8}{2x + 3} } = 2 \: \: or \: \: \sqrt{ \frac{3x + 8}{2x + 3} } = 3$

$\implies \: \frac{3x + 8}{2x + 3} = 4 \: \: or \: \: \frac{3x + 8}{2x + 3} = 9$

$\implies \: 3x + 8 = 4(2x +3 ) \: \: or \: \: 3x + 8 = 9(2x + 3)$

$\implies \: 3x + 8 = 8x +12 \: \: or \: \: 3x + 8 = 18x +27$

$\implies \: 5x + 4 = 0 \: \: or \: \: 15x + 19 = 0$

$\implies \: x = - \frac{4}{5} \: \: or \: \: x = - \frac{19}{15}$