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\(a,\sqrt{4x^2-4x+1}+\sqrt{4x^2-12x+9}\)
\(=\sqrt{\left(2x-1\right)^2}+\sqrt{\left(2x-3\right)^2}\)
\(=|2x-1|+|2x-3|\)
\(b,\sqrt{49x^2-42x+9}+\sqrt{49x^2+42x+9}\)
\(=\sqrt{\left(7x-3\right)^2}+\sqrt{\left(7x+3\right)^2}\)
\(=|7x-3|+|7x+3|\)
=.= hok tốt!!
\(B=\sqrt{16x+16}-\sqrt{9x+9}+\sqrt{4x+4}+\sqrt{x+1}\)
\(=4\sqrt{x+1}-3\sqrt{x+1}+2\sqrt{x+1}+\sqrt{x+1}\)
\(=\sqrt{x+1}\left(4-3+2+1\right)=4\sqrt{x+1}\)
ĐKXĐ: \(x\ge2\)
Từ pt đã cho suy ra:
\(7\sqrt{x-2}-2\sqrt{x-2}=3\sqrt{x-2}+8\)
⇒ \(2\sqrt{x-2}=8\) ⇒ \(x=18\)
\(=\left(2-\sqrt{3}\right)\left(\sqrt{3}+1\right)\sqrt{2}\left(\sqrt{2+\sqrt{3}}\right)\)
\(=\left(2-\sqrt{3}\right)\left(\sqrt{3}+1\right)\sqrt{2\left(2+\sqrt{3}\right)}\)
\(=\left(2\sqrt{3}+2-3-\sqrt{3}\right)\sqrt{4+2\sqrt{3}}\)
\(=\left(\sqrt{3}-1\right)\sqrt{3+2\sqrt{3}+1}\)
\(=\left(\sqrt{3}-1\right)\sqrt{\left(\sqrt{3}\right)^2+2\cdot\sqrt{3}\cdot1+1^2}\)
\(=\left(\sqrt{3}-1\right)\sqrt{\left(\sqrt{3}+1\right)^2}\)
\(=\left(\sqrt{3}-1\right)|\sqrt{3}+1|\)
\(=\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)\)
\(=\left(\sqrt{3}\right)^2-1^2\)
\(=3-1\)
\(=2\)
Lời giải:
$\sqrt{16x}-\sqrt{225a^3}+\sqrt{144xy^2}-\sqrt{49x}$
$=4\sqrt{x}-15\sqrt{a^3}+12\sqrt{xy^2}-7\sqrt{x}$
$=-3\sqrt{x}-15\sqrt{a^3}+12|y|\sqrt{x}$
$=\sqrt{x}(12|y|-3)-15\sqrt{a^3}$