Question

[Quyết Tâm Chiến Thắng]

Bài 1 Giải pt 

\(a,5\sqrt{2x^3+16}=2\left(x^2+8\right)\)

\(b,2\left(3x+5\right)\sqrt{x^2-9}=3x^2+2x+30\)

Bài 2: Cho x,y,z>0 thỏa mãn \(xy+yz+xz=1\) .Tính gt bt

\(P=x\sqrt{\frac{\left(1+y^2\right)\left(1+z^2\right)}{1+x^2}}+y\sqrt{\frac{\left(1+x^2\right)\left(1+z^2\right)}{1+y^2}+z\sqrt{\frac{\left(1+y^2\right)\left(1+x^2\right)}{1+z^2}}}\)

Answer 1

[Ngô Trí Nhân]

I am grade 5

Answer 2

[zZz Cool Kid_new zZz]

Khai  triển nó ra,ta có:

\(1+y^2=y^2+xy+yz+zx=\left(y+x\right)\left(y+z\right)\)

\(1+x^2=xy+yz+zx+x^2=\left(x+y\right)\left(x+z\right)\)

\(1+z^2=xy+yz+zx+z^2=\left(z+x\right)\left(z+y\right)\)

Ta có:\(P=\Sigma x\sqrt{\frac{\left(y+x\right)\left(y+z\right)\left(z+x\right)\left(z+y\right)}{\left(x+y\right)\left(x+z\right)}}\)

\(\Sigma x\cdot\left(y+z\right)\)

Rút gọn dc như vậy rồi chị làm nốt ạ