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 {114pm {sqrt {18496}}}{50}}}
{displaystyle x={frac {114pm 136}{50}}}
{displaystyle x _{1}=5}
{displaystyle x _{2}=-{frac {11}{25}}}  - не удовлетворяет

Ответ:  {displaystyle x=5}

Answer 2

{{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 {114pm {sqrt {18496}}}{50}}}
{x={frac {114pm 136}{50}}}
{x _{1}=5}
{x _{2}=-{frac {11}{25}}} - не удовлетворяет

Ответ: {x=5}

Answer 3

[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 {114pm {sqrt {18496}}}{50}}
[tex] x={frac {114pm 136}{50}}
[tex] x _{1}=5
[tex] x _{2}=-{frac {11}{25}} - не удовлетворяет

Ответ: x=5

Answer 4

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

Ответ: x=5