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c,\(\left(\frac{\sqrt{1+a}}{\sqrt{1+a}-\sqrt{1-a}}+\frac{1-a}{\sqrt{1-a^2}-1+a}\right)\left(\sqrt{\frac{1}{a^2}-1}-\frac{1}{a}\right)\)
\(=\left(\frac{\sqrt{1+a}}{\sqrt{1+a}-\sqrt{1-a}}+\frac{\sqrt{1-a}.\sqrt{1-a}}{\sqrt{1-a}\left(\sqrt{1+a}-\sqrt{1-a}\right)}\right)\left(\frac{\sqrt{1-a^2}-1}{a}\right)\)
\(=\frac{\left(\sqrt{1+a}+\sqrt{1-a}\right)^2}{\left(1+a\right)-\left(1-a\right)}.\frac{\left(\sqrt{1-a^2}-1\right)}{a}=-1\)
M chỉ làm tiếp thôi nha, ko chép lại đề với đk đâu
a,
\(=\frac{a+2\sqrt{ab}+b-4\sqrt{ab}}{\sqrt{a}-\sqrt{b}}-\)\(\frac{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{ab}}\)
\(=\frac{a-2\sqrt{ab}+b}{\sqrt{a}-\sqrt{b}}-\left(\sqrt{a}-\sqrt{b}\right)\)
\(=\frac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}-\sqrt{b}}-\sqrt{a}+\sqrt{b}\)
\(=\sqrt{a}-\sqrt{b}-\sqrt{a}+\sqrt{b}\)
\(=0\)
b,
\(=\left(a-b\right)\left(\sqrt{\frac{a+b}{a-b}}-1\right)\left(a-b\right)\left(\sqrt{\frac{a+b}{a-b}}+1\right)\)
\(=\left(a-b\right)^2\left(\frac{a+b}{a-b}-1\right)\)
\(=\left(a-b\right)^2\cdot\frac{a+b-a+b}{a-b}\)
\(=\left(a-b\right)2b=2ab-2b^2\)
1.\(5\sqrt{a}+6\sqrt{a.\frac{1}{4}}-\sqrt{a^2.\frac{4}{a}}+\sqrt{5}=5\sqrt{a}+6.\frac{1}{2}\sqrt{a}-2\sqrt{a}\)+\(\sqrt{5}\)
bạn tự làm nốt các câu này và làm tương tự các câu kia nhé!!Nếu khó chỗ nào hãy nhắn tin cho mk!! hihi
Bài 1:
a: \(=\sqrt{\dfrac{7-4\sqrt{3}}{2-\sqrt{3}}}\cdot\sqrt{2+\sqrt{3}}\)
\(=\sqrt{2-\sqrt{3}}\cdot\sqrt{2+\sqrt{3}}=1\)
Bài 2:
\(VT=\left(4+\sqrt{15}\right)\cdot\left(\sqrt{5}-\sqrt{3}\right)\cdot\sqrt{8-2\sqrt{15}}\)
\(=\left(4+\sqrt{15}\right)\left(8-2\sqrt{15}\right)\)
\(=32-8\sqrt{15}+8\sqrt{15}-30=2\)
\(\left(\frac{\sqrt{b}}{a-\sqrt{ab}}-\frac{\sqrt{a}}{\sqrt{ab-b}}\right).\left(a\sqrt{b}-b\sqrt{a}\right)\)
\(=\left(\frac{\sqrt{b}}{\sqrt{a}\sqrt{a}-\sqrt{a}\sqrt{b}}-\frac{\sqrt{a}}{\sqrt{a}\sqrt{b}-\sqrt{b}\sqrt{b}}\right).\left(\sqrt{a}\sqrt{a}\sqrt{b}-\sqrt{b}\sqrt{b}\sqrt{a}\right)\)
\(=\left(\frac{\sqrt{b}}{\sqrt{a}.\left(\sqrt{a}-\sqrt{b}\right)}-\frac{\sqrt{a}}{\sqrt{b}.\left(\sqrt{a}-\sqrt{b}\right)}\right).\sqrt{a}\sqrt{b}.\left(\sqrt{a}-\sqrt{b}\right)\)
\(=\left(\frac{\left(\sqrt{b}\right)^2}{\sqrt{a}\sqrt{b}.\left(\sqrt{a}-\sqrt{b}\right)}-\frac{\left(\sqrt{a}\right)^2}{\sqrt{a}\sqrt{b}.\left(\sqrt{a}\sqrt{b}\right)}\right).\sqrt{a}\sqrt{b}.\left(\sqrt{a}-\sqrt{b}\right)\)
\(=\frac{\left(\sqrt{b}\right)^2-\left(\sqrt{a}\right)^2}{\sqrt{a}\sqrt{b}.\left(\sqrt{a}-\sqrt{b}\right)}.\sqrt{a}\sqrt{b}.\left(\sqrt{a}-\sqrt{b}\right)\)
\(=\left(\sqrt{b}\right)^2-\left(\sqrt{b}\right)^2\)
\(=b-a\)
\(P=\frac{a+b}{\sqrt{a}+\sqrt{b}}:\left(\frac{a+b}{a-b}-\frac{\sqrt{b}}{\sqrt{b}-\sqrt{a}}+\frac{\sqrt{a}}{\sqrt{a}+\sqrt{b}}\right)-\frac{\left|\sqrt{a}-\sqrt{b}\right|}{2}\)
\(P=\frac{a+b}{\sqrt{a}+\sqrt{b}}:\left(\frac{a+b}{a-b}+\frac{\sqrt{b}\left(\sqrt{a}+\sqrt{b}\right)}{a-b}+\frac{\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)}{a-b}\right)-\frac{\left|\sqrt{a}-\sqrt{b}\right|}{2}\)
\(P=\frac{a+b}{\sqrt{a}+\sqrt{b}}:\left(\frac{a+b+\sqrt{ab}+b+a-\sqrt{ab}}{a-b}\right)-\frac{\left|\sqrt{a}-\sqrt{b}\right|}{2}\)
\(P=\frac{a+b}{\sqrt{a}+\sqrt{b}}:\left(\frac{2\left(a+b\right)}{a-b}\right)-\frac{\left|\sqrt{a}-\sqrt{b}\right|}{2}\)
\(P=\frac{\sqrt{a}-\sqrt{b}}{2}-\frac{\left|\sqrt{a}-\sqrt{b}\right|}{2}\)
TH1: \(a>b\Rightarrow P=\frac{\sqrt{a}-\sqrt{b}}{2}-\frac{\sqrt{a}-\sqrt{b}}{2}=0\)
TH2: \(0< a< b\Rightarrow P=\frac{\sqrt{a}-\sqrt{b}}{2}-\frac{\sqrt{b}-\sqrt{a}}{2}=\sqrt{a}-\sqrt{b}\)
\(D=\frac{\left(\sqrt{a}-\sqrt{b}\right)^2}{\sqrt{a}+\sqrt{b}}-\frac{a\sqrt{b}-b\sqrt{a}}{\sqrt{ab}}\)
\(=\frac{a-2\sqrt{ab}+b+4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-\frac{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{ab}}\)
\(=\frac{a+2\sqrt{ab}+b}{\sqrt{a}+\sqrt{b}}-\frac{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{ab}}\)
\(=\frac{\left(\sqrt{a}+\sqrt{b}\right)^2}{\sqrt{a}+\sqrt{b}}-\left(\sqrt{a}-\sqrt{b}\right)\)
\(=\sqrt{a}+\sqrt{b}-\sqrt{a}+\sqrt{b}\)
\(=2\sqrt{b}\)
\(D=\frac{\left(\sqrt{a}-\sqrt{b}\right)^2+4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-\frac{a\sqrt{b}-b\sqrt{a}}{\sqrt{ab}}\)
\(D=\frac{\left(\sqrt{a}-\sqrt{b}\right)^2+4\sqrt{ab}}{\sqrt{a}+\sqrt{b}}-\frac{-b+\sqrt{a}.\sqrt{b}}{\sqrt{b}}\)
\(D=\frac{\left[\left(\sqrt{a}-\sqrt{b}\right)^2+4\sqrt{ab}\right].\sqrt{b}}{\left(\sqrt{a}+\sqrt{b}\right).\sqrt{b}}-\frac{\left(\sqrt{a}.\sqrt{b}-b\right)\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{b}.\left(\sqrt{a}+\sqrt{b}\right)}\)
\(D=\frac{\left[\left(\sqrt{a}-\sqrt{b}\right)^2+4\sqrt{ab}\right]-\left(\sqrt{a}.\sqrt{b}-b\right)\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{b}.\left(\sqrt{a}+\sqrt{b}\right)}\)
\(D=\frac{2b.\sqrt{a}+2b.\sqrt{b}}{\sqrt{b}.\left(\sqrt{a}+\sqrt{b}\right)}\)
\(D=\frac{2b.\left(\sqrt{a}+\sqrt{b}\right)}{\sqrt{b}\left(\sqrt{a}+\sqrt{b}\right)}\)
\(D=2\sqrt{b}\)