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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 9: A=[(√a+3)/(√a+2) + (4a√a+3a+9)/(a-√a-6)] : [√a/(√a+3) + (2√a+3)/(a+5√a+6)] a)rút gọn. b )tìm a để A =48

Tháng Mười Một 25, 2022 Toán học 1 Comment 0 views

Toán Lớp 9: A=[(√a+3)/(√a+2) + (4a√a+3a+9)/(a-√a-6)] : [√a/(√a+3) + (2√a+3)/(a+5√a+6)]
a)rút gọn.
b )tìm a để A =48

Comments ( 1 )

  1. catlantuong
    catlantuong
    25 Tháng Mười Một, 2022 at 12:25 sáng
    Reply
    a-\sqrt{a}-6=a-3\sqrt{a}+2\sqrt{a}-6=\sqrt{a}(\sqrt{a}-3)+2(\sqrt{a}-3)=(\sqrt{a}-3)(\sqrt{a}+2)
    a+5\sqrt{a}+6=a+3\sqrt{a}+2\sqrt{a}+6=\sqrt{a}(\sqrt{a}+3)+2(\sqrt{a}+3)=(\sqrt{a}+3)(\sqrt{a}+2) 
    ĐKXĐ: a\ge0,a\ne9
    a, A=({\sqrt{a}+3}/{\sqrt{a}+2}+{4a\sqrt{a}+3a+9}/{a-\sqrt{a}-6}):({\sqrt{a}}/{\sqrt{a}+3}+{2\sqrt{a}+3}/{a+5\sqrt{a}+6})
    =[{\sqrt{a}+3}/{\sqrt{a}+2}+{4a\sqrt{a}+3a+9}/{(\sqrt{a}-3)(\sqrt{a}+2)}]:[{\sqrt{a}}/{\sqrt{a}+3}+{2\sqrt{a}+3}/{(\sqrt{a}+3)(\sqrt{a}+2)}]
    =[{(\sqrt{a}+3)(\sqrt{a}-3)}/{(\sqrt{a}-3)(\sqrt{a}+2)}+{4a\sqrt{a}+3a+9}/{(\sqrt{a}-3)(\sqrt{a}+2)}]:[{\sqrt{a}(\sqrt{a}+2)}/{(\sqrt{a}+3)(\sqrt{a}+2)}+{2\sqrt{a}+3}/{(\sqrt{a}+3)(\sqrt{a}+2)}]
    ={(\sqrt{a}+3)(\sqrt{a}-3)+4a\sqrt{a}+3a+9}/{(\sqrt{a}-3)(\sqrt{a}+2)}:{\sqrt{a}(\sqrt{a}+2)+2\sqrt{a}+3}/{(\sqrt{a}+3)(\sqrt{a}+2)}
    ={a-9+4a\sqrt{a}+3a+9}/{(\sqrt{a}-3)(\sqrt{a}+2)}:{a+2\sqrt{a}+2\sqrt{a}+3}/{(\sqrt{a}+3)(\sqrt{a}+2)}
    ={4a\sqrt{a}+4a}/{(\sqrt{a}-3)(\sqrt{a}+2)}:{a+4\sqrt{a}+3}/{(\sqrt{a}+3)(\sqrt{a}+2)}
    ={4a(\sqrt{a}+1)}/{(\sqrt{a}-3)(\sqrt{a}+2)}:{a+\sqrt{a}+3\sqrt{a}+3}/{(\sqrt{a}+3)(\sqrt{a}+2)}
    ={4a(\sqrt{a}+1)}/{(\sqrt{a}-3)(\sqrt{a}+2)}:{\sqrt{a}(\sqrt{a}+1)+3(\sqrt{a}+1)}/{(\sqrt{a}+3)(\sqrt{a}+2)}
    ={4a(\sqrt{a}+1)}/{(\sqrt{a}-3)(\sqrt{a}+2)}:{(\sqrt{a}+3)(\sqrt{a}+1)}/{(\sqrt{a}+3)(\sqrt{a}+2)}
    ={4a(\sqrt{a}+1)}/{(\sqrt{a}-3)(\sqrt{a}+2)}.{(\sqrt{a}+3)(\sqrt{a}+2)}/{(\sqrt{a}+3)(\sqrt{a}+1)}
    ={4a}/{\sqrt{a}-3}
    Vậy với a\ge0,a\ne9 thì A={4a}/{\sqrt{a}-3}
    b, A=48
    ⇒{4a}/{\sqrt{a}-3}=48
    ⇔{4a}/{\sqrt{a}-3}={48(\sqrt{a}-3)}/{\sqrt{a}-3}
    ⇒4a=48(\sqrt{a}-3)
    ⇔4a=48\sqrt{a}-144
    ⇔4a-48\sqrt{a}+144=0
    ⇔(2\sqrt{a})^2-2.2\sqrt{a}.12+12^2=0
    ⇔(2\sqrt{a}-12)^2=0
    ⇔2\sqrt{a}-12=0
    ⇔2\sqrt{a}=12
    ⇔\sqrt{a}=6
    ⇔a=36(TM)
    Vậy với a=36 thì A=48

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222-9+11+12:2*14+14 = ? ( )

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