Question

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giúp mình câu 2 và câu 3 gấp nhé

Answer 1

[Hoàng Như Quỳnh]

\(2.\)

\(a,1=\sqrt{1}\)

\(1< 2< =>\sqrt{1}< \sqrt{2}< =>1< \sqrt{2}\)

\(b,2-\sqrt{2}-1\)

\(1-\sqrt{2}\)

mà \(1< \sqrt{2}< =>1-\sqrt{2}< 0\)

\(2< \sqrt{2}+1\)

c, 7 và \(5\sqrt{2}\)

\(7=\sqrt{49}\)

\(5\sqrt{2}=\sqrt{50}< =>\sqrt{49}< \sqrt{50}\)

\(< =>7< 5\sqrt{2}\)

d, 7 và \(\sqrt{47}\)

\(7=\sqrt{49}< =>\sqrt{49}>\sqrt{47}\)

\(7>\sqrt{47}\)

e, 1 và \(\sqrt{3}-1\)

\(1-\sqrt{3}+1=2-\sqrt{3}=\sqrt{4}-\sqrt{3}>0\)

\(1>\sqrt{3}-1\)

f,\(2\sqrt{31}\)và \(10\)

\(2\sqrt{31}=\sqrt{124}\)

\(10=\sqrt{100}< =>\sqrt{124}>\sqrt{100}\)

\(2\sqrt{31}>10\)

\(3.A=\sqrt{1-4a+4a^2}-2a\)

\(A=\sqrt{\left(1-2a\right)^2}-2a\)

\(A=\left|1-2a\right|-2a\)

kết hợp với ĐKXĐ \(x\ge0,5\)

\(A=2a-1-2a=-1\)

\(b,B=\sqrt{x-2+2\sqrt{x-3}}\)

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

\(B=\sqrt{\left(\sqrt{x-1}+1\right)^2}\)

\(B=\left|\sqrt{x-1}+1\right|\)

kết hợp đkxđ

\(B=\sqrt{x-1}+1\)

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

\(C=\sqrt{\left(\sqrt{x}-1\right)^2}+\sqrt{\left(\sqrt{x}+1\right)^2}\)

\(C=\left|\sqrt{x}-1\right|+\left|\sqrt{x}+1\right|\)

\(TH1:0\le x\le1\)

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

\(TH2:x>1\)

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

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

\(D=\sqrt{\left(\sqrt{x-1}+1\right)^2}+\sqrt{\left(\sqrt{x-1}-1\right)^2}\)

\(D=\left|\sqrt{x-1}+1\right|+\left|\sqrt{x-1}-1\right|\)

kết hợp với đkxđ

\(TH1:1\le x\le4\)

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

\(TH2:x>4\)

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