(4x+5)^0,5-(14-x)^0,5=2 решите уравнение пажалуйста

Question

(4x+5)^0,5-(14-x)^0,5=2 решите уравнение пажалуйста

Answer 1

{\displaystyle {\sqrt {4x+5}}-{\sqrt {14-x}}=2}
{\displaystyle 4x+5-2{\sqrt {4x+5}}·{\sqrt {14-x}}+14-x=4}
{\displaystyle {\sqrt {56x-4^{2}}+70-5x}={\frac {3x+15}{2}}}
{\displaystyle -4x^{2}+51x+70={\frac {9x^{2}+90x+225}{4}}}
{\displaystyle -16x^{2}+204x+280=9x^{2}+90x+225}
{\displaystyle 25x^{2}-114x-55=0}
{\displaystyle D=(-114)^{2}+4·25·55=12996+5500=18496}
{\displaystyle x={\frac {114\pm \{\sqrt {18496}}}{50}}}
{\displaystyle x={\frac {114\pm \136}{50}}}
{\displaystyle \x _{1}\=5}
{\displaystyle \x _{2}\=-{\frac {11}{25}}}  - не удовлетворяет

Ответ:  {\displaystyle x=5}

Comments

{{\sqrt {4x+5}}-{\sqrt {14-x}}=2}
{4x+5-2{\sqrt {4x+5}}•{\sqrt {14-x}}+14-x=4}
{{\sqrt {56x-4^{2}}+70-5x}={\frac {3x+15}{2}}}
{-4x^{2}+51x+70={\frac {9x^{2}+90x+225}{4}}}
{-16x^{2}+204x+280=9x^{2}+90x+225}
{25x^{2}-114x-55=0}
{D=(-114)^{2}+4•25•55=12996+5500=18496}
{x={\frac {114\pm \{\sqrt {18496}}}{50}}}
{x={\frac {114\pm \136}{50}}}
{\x _{1}\=5}
{\x _{2}\=-{\frac {11}{25}}} - не удовлетворяет

Ответ: {x=5}

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[tex] {\sqrt {4x+5}}-{\sqrt {14-x}}=2
[tex] 4x+5-2{\sqrt {4x+5}}•{\sqrt {14-x}}+14-x=4
[tex] {\sqrt {56x-4^{2}}+70-5x}={\frac {3x+15}{2}}
[tex] -4x^{2}+51x+70={\frac {9x^{2}+90x+225}{4}}
[tex] -16x^{2}+204x+280=9x^{2}+90x+225
[tex] 25x^{2}-114x-55=0
[tex] D=(-114)^{2}+4•25•55=12996+5500=18496
[tex] x={\frac {114\pm \{\sqrt {18496}}}{50}}
[tex] x={\frac {114\pm \136}{50}}
[tex] \x _{1}\=5
[tex] \x _{2}\=-{\frac {11}{25}} - не удовлетворяет

Ответ: x=5

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[tex] \sqrt {4x+5}-\sqrt {14-x}=2 [/tex]
[tex] 4x+5-2\sqrt {4x+5}•\sqrt {14-x}+14-x=4 [/tex]
[tex] \sqrt {56x-4^{2}+70-5x }=\frac {3x+15}{2} [/tex]
[tex] -4x^{2}+51x+70=\frac {9x^{2}+90x+225}{4} [/tex]
[tex] -16x^{2}+204x+280=9x^{2}+90x+225 [/tex]
[tex] 25x^{2}-114x-55=0 [/tex]
[tex] D=(-114)^{2}+4•25•55=12996+5500=18496 [/tex]
[tex] x=\frac {114\pm \\sqrt {18496}}{50} [/tex]
[tex] x=\frac {114\pm \136}{50} [/tex]
[tex] \x _{1}\=5 [/tex]
[tex] \x _{2}\=-\frac {11}{25} [/tex] - не удовлетворяет

Ответ: x=5