Question

Решите уравнение:
$a) 5x-18 sqrt{x} -8=0$
$b) sqrt{33-8x} =x$
$c) 3x-2 sqrt{x} -8=0$
$d)sqrt{2x+15} =x$

Answer 1

$5x-18 sqrt{x} -8=0 \ D_1=9^2+5cdot8=121 \ sqrt{x} = frac{9+11}{5} =4 \ sqrt{x} neq frac{9-11}{5} =-0.4 \ x=4^2=16$
Ответ: 16

$sqrt{33-8x} =x \ left { {{33-8x=x^2} atop {x geq 0}} right. \ left { {{x^2+8x-33=0} atop {x geq 0}} right. \ left { {{D_1=4^2+33=49} atop {x geq 0}} right. \ left { {{x=-4pm7} atop {x geq 0}} right. \ left { {{x=-11; x=3} atop {x geq 0}} right. \ x=3$
Ответ: 3

$3x-2 sqrt{x} -8=0 \ D_1=1+3cdot8=25 \ sqrt{x} = frac{1+5}{3} =2 \ sqrt{x} neq frac{1-5}{3} =- frac{4}{3} \ x=2^2=4$
Ответ: 4

$sqrt{2x+15} =x \ left { {{2x+15=x^2} atop {x geq 0}} right. \ left { {{x^2-2x-15=0} atop {x geq 0}} right. \ left { {{D_1=1+15=16} atop {x geq 0}} right. \ left { {{x=1pm4} atop {x geq 0}} right. \ left { {{x=-3; x=5} atop {x geq 0}} right. \ x=5$
Ответ: 5