Question

[phonie]

giúp mình bài này với mình đang cần gấp

Answer 1

[YangSu]

\(a,C=\left(\dfrac{4\sqrt{x}}{2+\sqrt{x}}+\dfrac{8x}{4-x}\right):\left(\dfrac{\sqrt{x}-1}{x-8\sqrt{x}}-\dfrac{2}{\sqrt{x}}\right)\left(dk:x>0,x\ne4,x\ne64\right)\)

\(=\left(\dfrac{4\sqrt{x}\left(2-\sqrt{x}\right)+8x}{4-x}\right):\left(\dfrac{\sqrt{x}-1-2\left(\sqrt{x}-8\right)}{\sqrt{x}\left(\sqrt{x}-8\right)}\right)\)

\(=\dfrac{8\sqrt{x}-4x+8x}{4-x}.\dfrac{\sqrt{x}\left(\sqrt{x}-8\right)}{\sqrt{x}-1-2\sqrt{x}+16}\)

\(=\dfrac{8\sqrt{x}+4x}{4-x}.\dfrac{\sqrt{x}\left(\sqrt{x}-8\right)}{-\sqrt{x}+15}\)

\(=\dfrac{4\sqrt{x}\left(2+\sqrt{x}\right)}{\left(2-\sqrt{x}\right)\left(2+\sqrt{x}\right)}.\dfrac{\sqrt{x}\left(\sqrt{x}-8\right)}{15-\sqrt{x}}\)

\(=\dfrac{4x\left(\sqrt{x}-8\right)}{ \left(2-\sqrt{x}\right)\left(15-\sqrt{x}\right)}\\ =\dfrac{4x\sqrt{x}-32x}{30-2\sqrt{x}-15\sqrt{x}+x}\\ =\dfrac{4x\sqrt{x}-32}{x-17\sqrt{x}+30}\)

\(b,C=-1\Leftrightarrow\dfrac{4x\sqrt{x}-32}{x-17\sqrt{x}+30}=-1\\ \Leftrightarrow4x\sqrt{x}-32+x-17\sqrt{x}+30=0\)

\(\Leftrightarrow4x\sqrt{x}-17\sqrt{x}+x-2=0\\ \Leftrightarrow x=4\left(ktmdk\right)\)

Vậy không có giá trị x thỏa mãn đề bài.