Question

[Rob Lucy]

ai làm hộ mk bài 9

Answer 1

[Phương An]

9a)

\(a-b=\sqrt{29+12\sqrt{5}}-2\sqrt{5}\)

\(=\sqrt{\left(2\sqrt{5}+3\right)^2}-2\sqrt{5}\)

\(=2\sqrt{5}+3-2\sqrt{5}\)

= 3

\(M=a^2\left(a+1\right)-b^2\left(b-1\right)-11ab+2015\)

\(=\left(a^3-b^3\right)-9ab+\left(a^2-2ab+b^2\right)+2015\)

\(=\left(a-b\right)^3+3ab\left(a-b\right)+\left(a-b\right)^2-9ab+2015\)

\(=\left(a-b\right)^3+\left(a-b\right)^2+3ab\left(a-b-3\right)+2015\)

\(=\left(3\right)^3+\left(3\right)^2+3ab\left(3-3\right)+2015\)

= 2051

Answer 2

[Nguyễn Như Ý]

Câu 9 .2)

Có: \(xy+\sqrt{\left(1+x^2\right)\left(1+y^2\right)}=1\)

\(\Leftrightarrow\) \(\sqrt{\left(1+x^2\right)\left(1+y^2\right)}=1-xy\)

\(\Leftrightarrow\) \(\left(1+x^2\right)\left(1+y^2\right)=\left(1-xy\right)^2\)

\(\Leftrightarrow\) \(1+x^2+y^2+x^2y^2=1-2xy+x^2y^2\)

\(\Leftrightarrow\) \(x^2+y^2=-2xy\)

\(\Leftrightarrow\) \(x^2+y^2+2xy=0\)

\(\Leftrightarrow\) \(\left(x+y\right)^2=0\)

\(\Leftrightarrow\) \(x+y=0\Leftrightarrow y=-x\)

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

\(=x\sqrt{1+x^2}-x\sqrt{1+x^2}=0\left(đpcm\right)\)