Question

Rezolvati urmatoarele ecuatii irationale
$\sqrt{2x - 1} - \sqrt{x - 1} = \sqrt{2x - 9}$
Va rog urgent!!!​

Answer 1

$\frac{2 \sqrt{x + 3} + \sqrt{x + 10} }{3 \sqrt{x + 3} - \sqrt{x + 10} } = 2$

$2 \sqrt{x + 3} + \sqrt{x + 10} = 2(3 \sqrt{x + 3} - \sqrt{x + 10} )$

$2 \sqrt{x + 3} + \sqrt{x + 10} = 6 \sqrt{x + 3} - 2 \sqrt{x + 10}$

$2 \sqrt{x + 3} - 6\sqrt{x + 3} = - 2 \sqrt{x + 10} - \sqrt{x + 10}$

$- 4 \sqrt{x + 3} = - 3 \sqrt{x + 10}$

$16(x + 3) = 9(x + 10)$

$16x + 48 = 9x + 90$

$16x - 9x = 90 - 48$

$7x = 42$

$x = 42 \div 7$

$x = 6$

Answer 2

Răspuns:

• x = 6

Explicație pas cu pas:

Salutare!

$\bf \dfrac{2\sqrt{x+3}+\sqrt{x+10} }{3\sqrt{x+3}-\sqrt{x+10}}=2\:\:\:\:\:\:\:\Big|\cdot(3\sqrt{x+3}-\sqrt{x+10})$

$\bf 2\sqrt{x+3}+\sqrt{x+10}=2\cdot(3\sqrt{x+3}-\sqrt{x+10})$

$\bf 2\sqrt{x+3}+\sqrt{x+10}=6\sqrt{x+3}-2\sqrt{x+10}$

$\bf 2\sqrt{x+3}+\sqrt{x+10}+2\sqrt{x+10}=6\sqrt{x+3}$

$\bf 2\sqrt{x+3}+3\sqrt{x+10}=6\sqrt{x+3}$

$\bf 3\sqrt{x+10}=6\sqrt{x+3}-2\sqrt{x+3}$

$\bf 3\sqrt{x+10}=4\sqrt{x+3}\:\:\:\:\:\:\:\:\Big|^{2}$

$\bf (3\sqrt{x+10})^{2}=(4\sqrt{x+3})^{2}$

$\bf 9\cdot(x+10)=16\cdot(x+3)$

$\bf 9x+90=16x+48$

$\bf 9x+90-48=16x$

$\bf 9x+42=16x$

$\bf 42=16x- 9x$

$\bf 42=7x\:\:\:\:\Big|:7$

$\boxed{\bf x=6}$

==pav38==