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\(=\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)\)
`4a+1(a<=0=>-a>=0)`
`=1-4(-a)`
`=1-(2sqrt{-a})^2`
`=(1-2sqrt{-a})(1+2sqrt{-a})`
i) \(=x\left(x-5\right)+3\left(x-5\right)=\left(x-5\right)\left(x+3\right)\)
j) \(=x\left(x-1\right)+8\left(x-1\right)=\left(x-1\right)\left(x+8\right)\)
k) \(=x\left(x+1\right)+3\left(x+1\right)=\left(x+1\right)\left(x+3\right)\)
l) \(=x\left(x-3\right)-2\left(x-3\right)=\left(x-3\right)\left(x-2\right)\)
m) \(=x\left(x^2-4x+4\right)=x\left(x-2\right)^2\)
\(=x\left(x^2-2x+1-y^2\right)=x\left[\left(x-1\right)^2-y^2\right]=x\left(x-1-y\right)\left(x-1+y\right)\)
3: \(=\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}=\sqrt{5}-\sqrt{3}\)
4: \(=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}=\sqrt{5}+\sqrt{3}\)
\(=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)\)
\(=\left(\sqrt{b}-1\right)\left(\sqrt{a}-1\right)\)
\(\sqrt{ab}-\sqrt{a}-\sqrt{b}+1\)
\(=\left(\sqrt{ab}-\sqrt{a}\right)-\left(\sqrt{b}-1\right)\)
\(=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)\)
\(=\left(\sqrt{b}-1\right)\left(\sqrt{a}-1\right)\)
12) \(\sqrt{11+2\sqrt{30}}=\sqrt{\left(\sqrt{6}\right)^2+2.\sqrt{6}.\sqrt{5}+\left(\sqrt{5}\right)^2}\)
\(=\sqrt{\left(\sqrt{6}+\sqrt{5}\right)^2}=\sqrt{6}+\sqrt{5}\)
\(=\sqrt{6+2\cdot\sqrt{6}\cdot\sqrt{5}+5}\)
\(=\sqrt{\left(\sqrt{6}+\sqrt{5}\right)^2}=\sqrt{6}+\sqrt{5}\)
hơi dài tí ^^
a10 + a5 + 1
= a10 - a9 + a7 - a6 + a5 - a3 + a2 + a9 - a8 + a6 - a5 + a4 - a3 + a + a8 - a7 + a5 - a4 + a2 - a + 1
nhóm 7 hạng tử ta đc :
= a2(a8 - a7 + a5 - a4 + a3 - a + 1) + a(a8 - a7 + a5 - a4 + a3 - a + 1) + (a8 - a7 + a5 - a4 + a3 - a + 1)
= (a2 + a + 1)(a8 - a7 + a5 - a4 + a3 - a + 1)
ĐKXĐ : \(-4\le x\le4\)
\(\Rightarrow\frac{x^3}{\sqrt{16-x^2}}=16-x^2\)
\(\Rightarrow x^3=\left(16-x^2\right)\left(\sqrt{16-x^2}\right)\)
\(\Rightarrow x^3=\left(\sqrt{16-x^2}\right)^3\)
\(\Rightarrow x=\sqrt{16-x^2}\)
\(\Rightarrow16-x^2=x^2\)
\(\Rightarrow2x^2=16\Rightarrow x^2=8\Rightarrow x=+-\sqrt{8}\)(thỏa)