\(\Leftrightarrow\left(1+x\sqrt{x^2+1}\right)\left(\sqrt{x^2+1}-x\right)=\left(\sqrt{x^2+1}-x\right)\left(\sqrt{x^2+1}+x\right)\)
\(\Leftrightarrow\left(\sqrt{x^2+1}-x\right)\left(1+x\sqrt{x^2+1}-\sqrt{x^2+1}-x\right)=0\)
\(\Leftrightarrow\left(\sqrt{x^2+1}-x\right)\left(\sqrt{x^2+1}-1\right)\left(x-1\right)=0\)
Tự giải tiếp nhé
Giải phương trình :
\(\frac{2\left(x-\sqrt{2}\right)\left(x-\sqrt{3}\right)}{\left(1-\sqrt{2}\right)\left(1-\sqrt{3}\right)}+\frac{3\left(x-1\right)\left(x-\sqrt{3}\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}-\sqrt{3}\right)}+\frac{4\left(x-1\right)\left(x-\sqrt{2}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-\sqrt{2}\right)}=3x-1\) .
giải pt: \(\left(\sqrt{x+5}-\sqrt{x+2}\right)\left(1+\sqrt{x^2+7x+10}\right)=3\)
giải pt
\(\frac{2\left(x-\sqrt{2}\right)\left(x-\sqrt{3}\right)}{\left(1-\sqrt{2}\right)\left(1-\sqrt{3}\right)}+\frac{3\left(x-1\right)\left(x-\sqrt{3}\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}-\sqrt{3}\right)}+\frac{4\left(x-1\right)\left(x-\sqrt{2}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-2\right)}\)=3x-1
Áp dụng nội suy niu tơn để giải pt sau
\(\frac{2\left(x-\sqrt{2}\right)\left(x-\sqrt{3}\right)}{\left(1-\sqrt{2}\right)\left(1-\sqrt{3}\right)}+\frac{3\left(x-1\right)\left(x-\sqrt{3}\right)}{\left(\sqrt{2}-1\right)\left(\sqrt{2}-\sqrt{3}\right)}+\frac{4\left(x-1\right)\left(x-\sqrt{2}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-\sqrt{2}\right)}=3x-1\)
Giải phương trình :
\(x+1=\sqrt{2\left(x+1\right)+2\sqrt{2\left(x+1\right)+2\sqrt{4\left(x+1\right)}}}\)
Giải pt: \(\sqrt{1+\sqrt{1-x^2}}=\left[\left(\sqrt{1+x}\right)^3-\left(\sqrt{1-x}\right)^3\right]=2+\sqrt{1-x^2}\)
Rút gọn: \(A=\frac{\sqrt{1+\sqrt{1-x^2}}.\left[\sqrt{\left(1+x\right)^3}-\sqrt{\left(1-x\right)^3}\right]}{2+\sqrt{1-x^2}}\)
Giải giúp mk... Mk cần gấp.
Giải phương trình :
\(\sqrt{x\left(3x+1\right)}-\sqrt{x\left(x-1\right)}=2\sqrt{x^2}\)
Giải pt:
a)\(\sqrt{x+2}+\sqrt{x-2}+2\sqrt{x^2-4}=6-2x\)
b)\(\left(\sqrt{x+3}-\sqrt{x}\right)\left(\sqrt{1-x}+1\right)=1\)
c)\(\left(\sqrt{1+x}+\sqrt{1-x}\right)\left(2+2\sqrt{1-x^2}\right)=8\)
