Tìm x ko âm bt
a)\(\sqrt{x}>3\)
b)\(\sqrt{2x}< 3\)
c)\(2\sqrt{x}>\)
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a)\(\sqrt{\left(x-3\right)^2}=|x-3|\)(*)
TH1: x-3 \(\ge0\Leftrightarrow x\ge3\)
(*)=> |x - 3|=x-3
TH2 \(x-3< 0\Leftrightarrow x< 3\)
(*)=>|x-3|=-(x-3)=3-x
Vậy khi x\(\ge\)3 thì (*)=x-3
Khi x<3 thì (*)=3-x
b) ĐK: x<\(\dfrac{1}{3}\)
\(\sqrt{\left(3x+1\right)^2}+2x\\ =\left|3x+1\right|+2x\left(@\right)\)
TH1:3x+1\(\ge\)0\(\Leftrightarrow3x\ge-1\Leftrightarrow x\ge-\dfrac{1}{3}\)=>\(-\dfrac{1}{3}\le x\le\dfrac{1}{3}\)
(@)=>|3x+1|+2x
=3x+1+2x
=5x+1
TH2 \(3x+1< 0\Leftrightarrow3x< -1\Leftrightarrow x< -\dfrac{1}{3}\)
(@)=>|3x+1|+2x
= -3x-1+2x
= -x-1
c) tương tự như vậy
\(1.\sqrt{\left(\sqrt{3}-2\right)^2}+\sqrt{\left(1+\sqrt{3}\right)^2}=\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(1+\sqrt{3}\right)^2}=2-\sqrt{3}+1+\sqrt{3}=3\) \(2a.\sqrt{x^2-2x+1}=7\)
⇔ \(x^2-2x+1=49\)
⇔ \(x^2-2x-48=0\)
⇔ \(\left(x+6\right)\left(x-8\right)=0\)
⇔ \(x=8orx=-6\)
\(b.\sqrt{4x-20}-3\sqrt{\dfrac{x-5}{9}}=\sqrt{1-x}\)
⇔ \(2\sqrt{x-5}-\sqrt{x-5}=\sqrt{1-x}\)
⇔ \(x-5=1-x\)
⇔ \(x=3\left(KTM\right)\)
KL.............
xem gi
co ban nho cua toi
may bi loi unikey thong cam nha moi nguoi
hihi
a) \(\sqrt[3]{x}< 2\Leftrightarrow\left(\sqrt[3]{x}\right)^3< 2^3\Leftrightarrow x< 8\)
b) \(\sqrt[3]{2x-1}>-3\Leftrightarrow\left(\sqrt[3]{2x-1}\right)^3>\left(-3\right)^3\Leftrightarrow2x-1>-27\Leftrightarrow2x>-26\Leftrightarrow x>-13\)
c) \(\sqrt[3]{2-3x}\le1\Leftrightarrow\left(\sqrt[3]{2-3x}\right)^3\le1\Leftrightarrow2-3x\le1\Leftrightarrow3x\ge1\Leftrightarrow x\ge\frac{1}{3}\)
d) \(\sqrt[3]{3-4x}\ge5\Leftrightarrow\left(\sqrt[3]{3-4x}\right)^3\ge5^3\Leftrightarrow3-4x\ge125\Leftrightarrow4x\le-122\Leftrightarrow x\le-\frac{61}{2}\)
a: =>x>9
b: =>0<2x<9
=>0<x<9/2
c: Đề thiếu vế phải ròi bạn