Question

tìm giá trị của x để M>-6:M=\(\left(\frac{\sqrt{x}}{2}-\frac{1}{2\sqrt{x}}\right)\left(\frac{x-\sqrt{x}}{\sqrt{x}+1}-\frac{x+\sqrt{x}}{\sqrt{x}-1}\right)\)

Answer 1

ĐKXĐ: x > 0; x \(\ne\)1

M = \(\left(\frac{\sqrt{x}}{2}-\frac{1}{2\sqrt{x}}\right)\left(\frac{x-\sqrt{x}}{\sqrt{x}+1}-\frac{x+\sqrt{x}}{\sqrt{x}-1}\right)\)

M = \(\frac{\sqrt{x}.\sqrt{x}-1}{2\sqrt{x}}\cdot\frac{\left(x-\sqrt{x}\right)\left(\sqrt{x}-1\right)-\left(x+\sqrt{x}\right)\left(\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)

M = \(\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{2\sqrt{x}}\cdot\frac{x\sqrt{x}-2x+\sqrt{x}-x\sqrt{x}-2x-\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)

M = \(\frac{-4x}{2\sqrt{x}}=-2\sqrt{x}\)

M > -6 => \(-2\sqrt{x}+6>0\)

<=> \(-2\left(\sqrt{x}-3\right)>0\) <=> \(\sqrt{x}-3< 0\) <=>  \(x< 9\)

kết hợp với đk => 0 < x < 9 và x khác 1