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Solve 3sqrt(x) = 8/(sqrt(9x - 32)) + sqrt(9x - 32)​

Sagot :

MsStawberry

[tex] \huge \color{gray}{ \tt{answer}}[/tex]

[tex]x = 4[/tex]

Step-by-step explanation:

[tex]3 \sqrt{x} = \frac{8}{(9x - 32)} + \sqrt{(9x - 32)} [/tex]

  • move the expression to the left

[tex]3 \sqrt{x} - \frac{8}{ \sqrt{9x - 32} } - \sqrt{9x - 32} = 0[/tex]

  • transform the expression

[tex] \frac{3 \sqrt{(9x - 32 x)} - 8 - \sqrt{9x - 32} }{ \sqrt{9x - 32} } [/tex]

  • set the numerator

[tex]3 \sqrt{(9x - 32)x} - 8 - (9x - 32) = 0[/tex]

  • remove the parentheses

[tex]3 \sqrt{9 {x}^{2} - 32x} + 24 - 9x = 0[/tex]

  • move the expression to the right

[tex]3 \sqrt{9 {x}^{2} - 32x } - 24 + 9x[/tex]

  • divide both sides

[tex] \sqrt{9 {x}^{2} - 32x } = - 8 + 3x[/tex]

  • simplify the expression

[tex]9 {x}^{2} - 32x = 9 {x}^{2} - 48x + 64[/tex]

  • cancel equal terms

[tex] - 32x = - 48x + 64[/tex]

  • move the variable to the left

[tex] - 32x = + 48x = 64[/tex]

  • collect like terms

[tex]16x = 64[/tex]

  • divide both sides

[tex] = \: \: x = 4[/tex]

  • check the solution

[tex]3 \sqrt{4} = \frac{8}{ \sqrt{9 \times 4 - 32} } + \sqrt{9 \times 4 - 32} [/tex]

  • simplify

[tex]6 = 6[/tex]

  • so the solution is

[tex]≈ \: \: x = 4[/tex]

[tex] \huge \color {cyan}{ \tt{hope \: \: it \: \: helps}}[/tex]

devishri1977

Answer:

Step-by-step explanation:

[tex]3\sqrt{x}=\frac{8}{\sqrt{9x-32}}+\sqrt{9x -32}\\\\\\3\sqrt{x}=\frac{8*\sqrt{9x-32}}{(\sqrt{9x-32})*(\sqrt{9x-32})}+\sqrt{9x-32}\\\\3\sqrt{x}=\frac{8*\sqrt{9x-32}}{9x-32}+\sqrt{9x-32}\\\\\\3\sqrt{x}=(\sqrt{9x-32})(\frac{8}{9x-32}+1)\\\\\frac{3\sqrt{x}}{\sqrt{9x-32}}=\frac{8+9x-32}{9x-32}\\\\\frac{3\sqrt{x}}{\sqrt{9x-32}}=\frac{9x - 24}{9x-32}\\\\Take \ square\\\\(\frac{3\sqrt{x}}{\sqrt{9x-32}})^{2}=(\frac{9x-24}{9x-32})^{2}\\\\\frac{9x}{9x-32}=\frac{(9x-24)^{2}}{(9x-32)^{2}}\\\\[/tex]

9x*(9x - 32) = (9x- 24)²

9x*9x - 9x*32 = 81x² - 2*9x*24 + 576

81x² - 288x = 81x² - 432x + 576

81x² - 288x - 81x² + 432x - 576 = 0

81x² - 81x² - 288x + 432x - 576 = 0

144x - 576 = 0

144x = 576

x = 576/144

x =4

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