Toán Lớp 9: a ) căn (4x+1)=x+1 b) căn (x^2 -10x +25) =x+3

Question

Toán Lớp 9:  a ) căn (4x+1)=x+1 b) căn (x^2 -10x +25) =x+3

phuongthuydung · Answer

a)  sqrt{4x+1}=x+1 (x&ge;-1/4)   &hArr;( sqrt{4x+1})^2=(x+1)^2   &hArr;4x+1-(x+1)^2=0   &hArr;4x+1-x^2-2x-1=0   &hArr;-x^2+2x=0   &hArr;-x(x-2)=0   &hArr; ( left[  begin{array}{l}-x=0  x-2=0 end{array}  right. )   &hArr; ( left[  begin{array}{l}x=0(TM)  x=2(TM) end{array}  right. )    Vậy S={0,2}   b)  sqrt{x^2-10x+25}=x+3 (x&ge;-3)   &hArr; sqrt{(x-5)^2}=x+3   &hArr;|x-5|=x+3   &hArr; ( left[  begin{array}{l}x-5=x+3  5-x=x+3 end{array}  right. )    &hArr; ( left[  begin{array}{l}0x=8(v&ocirc; l&yacute;)  x=1(TM) end{array}  right. )     Vậy S={1}

tuyetnhungthu · Answer

Giải đáp+Lời giải và giải thích chi tiết a) sqrt{4x+1}=x+1(x>=-1/4) <=>4x+1=x^2+2x+1 <=>x^2+2x+1-4x-1=0 <=>x^2-2x=0 <=>x(x-2)=0 <=>[(x=0(tm)),(x=2(tm)):} Vậy S={0;2} b) sqrt{x^2-10x+25}=x+3(x>=-3) <=> sqrt{(x-5)^2}=x+3 <=>|x-5|=x+3 <=>[(x-5=x+3),(5-x=x+3):} <=>[(-5=3(loại)),(2x=2):} <=>x=1(tm) Vậy S={1}