Question

x=(1-căn4)(1-căn16)(1-căn36)(1-căn64)(1-căn100)

y=căn0.1

so sánh x,y

Answer 1

\(x=\left(1-\sqrt{4}\right)\left(1-\sqrt{16}\right)\left(1-\sqrt{36}\right)\left(1-\sqrt{64}\right)\left(1-\sqrt{100}\right)\)

= (1 - 2)(1 - 4)(1 - 6)(1 - 8)(1 - 10)

= -1 . (-3) . (-5) . (-7) . (-9) (số âm)

\(y=\sqrt{0,1}=\sqrt{\dfrac{1}{10}}=\dfrac{1}{\sqrt{10}}\)

(số dương)

=> x < y

Answer 2

\(x=\left(1-\sqrt{4}\right)\left(1-\sqrt{16}\right)\left(1-\sqrt{36}\right)\left(1-\sqrt{64}\right)\left(1-\sqrt{100}\right)\\ =\left(1-2\right)\left(1-4\right)\left(1-6\right)\left(1-8\right)\left(1-10\right)\\ =\left(-1\right)\left(-3\right)\left(-5\right)\left(-7\right)\left(-9\right)< 0< \sqrt{0.1}=y\\ \Rightarrow x< y\)