Toán Lớp 9: Giải phương trình: x-2 √x-3=3

Question

Toán Lớp 9:  Giải phương trình: x-2 ​​​​√x-3=3

behocgioitoan · Answer

x - 2 sqrt{x - 3} = 3   ĐKXĐ: x >= 3   &hArr; x - 3 - 2 sqrt{x - 3} = 0   &hArr; ( sqrt{x - 3})&sup2; - 2 sqrt{x - 3} = 0   &hArr; ( sqrt{x - 3})( sqrt{x - 3}) - 2 sqrt{x - 3} = 0   &hArr; ( sqrt{x - 3})( sqrt{x - 3} - 2) = 0   &hArr; $ left[ begin{matrix}  sqrt{x - 3} = 0    sqrt{x - 3} - 2 = 0 end{matrix} right.$   &hArr; $ left[ begin{matrix} x - 3= 0    sqrt{x - 3} = 2 end{matrix} right.$   &hArr; $ left[ begin{matrix} x = 3 (TM)   x = 7 (TM) end{matrix} right.$

baoquyen · Answer

x    &minus;    2      &radic;      x    &minus;    3        =    3     (     Đ     KXD    :    x    &ge;    3    )                  &hArr;    2      &radic;      x    &minus;    3        =    x    &minus;    3            &hArr;2x-3=x-3            &hArr;      &radic;      x    &minus;    3         (      &radic;      x    &minus;    3        &minus;    2    )     =    0            &hArr;x-3(x-3-2)=0            &hArr;      &radic;      x    &minus;    3        =    0            &hArr;x-3=0     hoặc            &radic;      x    &minus;    3        =    2       x-3=2            &hArr;    x    &minus;    3    =    0            &hArr;x-3=0     hoặc          x    &minus;    3    =    4       x-3=4       &hArr;x=3     hoặc          x    =    7