Giải phương trình

a, \(\sqrt[3]{x^2-1}+3=\sqrt{x^3-2}.\)

b, \(x^2-x-2\sqrt{1+16x}=2\)

c, \(\left(x-3\right)\left(x+1\right)+3\left(x-2\right).\sqrt{\frac{x+1}{x-3}=4}\)

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

e, \(x+\sqrt{x+\frac{1}{2}+\sqrt{x+\frac{1}{4}}=2}\)

Giải dùm với 1 câu cũng được cảm ơn tik nhiệt tình

Giải phương trình

a, \(\sqrt[3]{x^2-1}+3=\sqrt{x^3-2}.\)

b, \(x^2-x-2\sqrt{1+16x}=2\)

c, \(\left(x-3\right)\left(x+1\right)+3\left(x-2\right).\sqrt{\frac{x+1}{x-3}=4}\)

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

e, \(x+\sqrt{x+\frac{1}{2}+\sqrt{x+\frac{1}{4}}=2}\)

Giải dùm với 1 câu cũng được Toán khó

\[D=\left ( \frac{1}{3\sqrt{x}-6} +\frac{1}{x-2\sqrt{x}}\right )\left ( \frac{1}{6} +\frac{1}{2\sqrt{x}}\right )\\ D=\left ( \frac{1}{3\left ( \sqrt{x}-2 \right )} +\frac{1}{\sqrt{x}\left ( \sqrt{x}-2 \right )}\right ).\frac{\sqrt{x}+3}{6\sqrt{x}}\\ D=\frac{\sqrt{x}+3}{3\sqrt{x}\left ( \sqrt{x}-2 \right )}.\frac{\sqrt{x}+3}{6\sqrt{x}}\\ D=\frac{\left ( \sqrt{x}+3 \right )^{2}}{18x\left ( \sqrt{x}-2 \right )}\\ D=\frac{x+6\sqrt{x}+9}{18x\sqrt{x}-36x}\]

A/ Đúng

B/ Sai

Mình rút gọn như thế này đúng không nhỉ?

\(P=\left(2-\frac{\sqrt{x}-1}{2\sqrt{x}-3}\right):\left(\frac{6\sqrt{x}+1}{2x-\sqrt{x}-3}+\frac{\sqrt{x}}{\sqrt{x}+1}\right)\)

\(P=\left[\frac{2\left(2\sqrt{x}-3\right)}{2\sqrt{x}-3}-\frac{\sqrt{x}-1}{2\sqrt{x}-3}\right]:\left[\frac{6\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-3\right)}+\frac{\sqrt{x}\left(2\sqrt{x}-3\right)}{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-3\right)}\right]\)

\(P=\left(\frac{4\sqrt{x}-6}{2\sqrt{x}-3}-\frac{\sqrt{x}-1}{2\sqrt{x}-3}\right):\left(\frac{6\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-3\right)}+\frac{2x-3\sqrt{x}}{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-3\right)}\right)\)

\(P=\left(\frac{4\sqrt{x}-6-\sqrt{x}+1}{2\sqrt{x}-3}\right):\left(\frac{6\sqrt{x}+1+2x-3\sqrt{x}}{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-3\right)}\right)\)

\(P=\frac{3\sqrt{x}-5}{2\sqrt{x}-3}:\frac{2x+3\sqrt{x}+1}{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-3\right)}\)

\(P=\frac{3\sqrt{x}-5}{2\sqrt{x}-3}.\frac{\left(\sqrt{x}+1\right)\left(2\sqrt{x}-3\right)}{2x+3\sqrt{x}+1}\)

\(P=\left(3\sqrt{x}-5\right).\frac{\left(\sqrt{x}+1\right)}{2x+3\sqrt{x}+1}\)

\(P=\frac{3x+3\sqrt{x}-5\sqrt{x}-5}{2x+3\sqrt{x}+1}\)

\(P=\frac{3x-5\sqrt{x}-5}{2x+1}\)

Giải phương trình

a, \(\sqrt[3]{x^2-1}+3=\sqrt{x^3-2}.\)

b, \(x^2-x-2\sqrt{1+16x}=2\)

c, \(\left(x-3\right)\left(x+1\right)+3\left(x-2\right).\sqrt{\frac{x+1}{x-3}=4}\)

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

e, \(x+\sqrt{x+\frac{1}{2}+\sqrt{x+\frac{1}{4}}=2}\)

Giải dùm với 1 câu cũng được cảm ơn tik nhiệt tình

Toán khó