Question

Giải các phương trình sau:

a,\(\sqrt{2x+3}+\sqrt{2x+2}=1\)

b,\(\sqrt{1-x}+\sqrt{4+x}=3\)

c,\(\sqrt{x+4}-\sqrt{2x-6}=1\)

d,\(\sqrt{3x-5}+\sqrt{2x+3}=\sqrt{x+2}\)

e,\(\sqrt{x-2}+\sqrt{x-1}=\sqrt{2x-3}\)

f,\(\sqrt{3x+7}-\sqrt{x+1}=2\)

Giúp mk với nhá các bạn ơi

Answer 1

\(\sqrt{x-2}+\sqrt{x-1}=\sqrt{2x-3}\)

\(\Leftrightarrow\sqrt{2x-3}-\sqrt{x-1}-\sqrt{x-2}=0\)

\(\Leftrightarrow\dfrac{2x-3-x+1}{\sqrt{2x-3}+\sqrt{x-1}}-\sqrt{x-2}=0\)

\(\Leftrightarrow\dfrac{x-2}{\sqrt{2x-3}+\sqrt{x-1}}-\dfrac{x-2}{\sqrt{x-2}}=0\)

\(\Leftrightarrow\left(x-2\right)\left(\dfrac{1}{\sqrt{2x-3}+\sqrt{x-1}}-\dfrac{1}{\sqrt{x-2}}\right)=0\)

Pt \(\dfrac{1}{\sqrt{2x-3}+\sqrt{x-1}}-\dfrac{1}{\sqrt{x-2}}=0\) vô nghiệm

=> x - 2 = 0

<=> x = 2 (nhận)

Answer 2

\(\sqrt{1-x}+\sqrt{4+x}=3\)

\(\Leftrightarrow\sqrt{1-x}-1+\sqrt{4+x}-2=0\)

\(\Leftrightarrow\dfrac{1-x-1}{\sqrt{1-x}+1}+\dfrac{4+x-4}{\sqrt{4+x}+\sqrt{2}}=0\)

\(\Leftrightarrow\dfrac{x}{\sqrt{4+x}+\sqrt{2}}-\dfrac{x}{\sqrt{1-x}+1}=0\)

\(\Leftrightarrow x\left(\dfrac{1}{\sqrt{4+x}+\sqrt{2}}-\dfrac{1}{\sqrt{1-x}+1}\right)=0\)

Pt \(\dfrac{1}{\sqrt{4+x}+\sqrt{2}}-\dfrac{1}{\sqrt{1-x}+1}=0\) vô nghiệm

=> x = 0

Answer 3

\(\sqrt{x+4}-\sqrt{2x-6}=1\)

\(\Leftrightarrow\sqrt{x+4}-3-\sqrt{2x-6}+2=0\)

\(\Leftrightarrow\dfrac{x+4-9}{\sqrt{x+4}+3}-\dfrac{2x-6-4}{\sqrt{2x-6}+2}=0\)

\(\Leftrightarrow\dfrac{x-5}{\sqrt{x+4}+3}-\dfrac{2\left(x-5\right)}{\sqrt{2x-6}+2}=0\)

\(\Leftrightarrow\left(x-5\right)\left(\dfrac{1}{\sqrt{x+4}+3}-\dfrac{2}{\sqrt{2x-6}+2}\right)=0\)

Pt \(\dfrac{1}{\sqrt{x+4}+3}-\dfrac{2}{\sqrt{2x-6}+2}=0\) vô nghiệm

=> x - 5 = 0

<=> x = 5 (nhận)

Answer 4

\(\sqrt{2x+3}+\sqrt{2x+2}=1\)

\(\Leftrightarrow\sqrt{2x+3}-1+\sqrt{2x+2}=0\)

\(\Leftrightarrow\dfrac{2x+3-1}{\sqrt{2x+3}-1}+\dfrac{2x+2}{\sqrt{2x+2}}=0\)

\(\Leftrightarrow\dfrac{2\left(x+1\right)}{\sqrt{2x+3}-1}+\dfrac{2\left(x+1\right)}{\sqrt{2x+2}}=0\)

\(\Leftrightarrow2\left(x+1\right)\left(\dfrac{1}{\sqrt{2x+3}-1}+\dfrac{1}{\sqrt{2x+2}}\right)=0\)

Pt \(\dfrac{1}{\sqrt{2x+3}-1}+\dfrac{1}{\sqrt{2x+2}}=0\) vô nghiệm

=> x + 1 = 0

<=> x = -1

Answer 5

\(\sqrt{3x+7}-\sqrt{x+1}=2\)

\(\Leftrightarrow\sqrt{3x+7}-2-\sqrt{x+1}=0\)

\(\Leftrightarrow\dfrac{3x+7-4}{\sqrt{3x+7}+2}-\dfrac{x+1}{\sqrt{x+1}}=0\)

\(\Leftrightarrow\dfrac{3\left(x+1\right)}{\sqrt{3x+7}+2}-\dfrac{x+1}{\sqrt{x+1}}=0\)

\(\Leftrightarrow\left(x+1\right)\left(\dfrac{3}{\sqrt{3x+7}+2}-\dfrac{1}{\sqrt{x+1}}\right)=0\)

Pt \(\dfrac{3}{\sqrt{3x+7}+2}-\dfrac{1}{\sqrt{x+1}}=0\) vô nghiệm

=> x + 1 = 0

<=> x = - 1 (nhận)