Tính :a, \((\sqrt{2}-\sqrt{3}).\left(\sqrt{2}+\sqrt{3}\right)\)b, \(-(\sqrt{2})^4+\left(\sqrt{3}\right)^6\)c , \(A=\frac{1}{1-\frac{1}{1-2^{-4}}}+\frac{1}{1+\frac{1}{1+2^{-1}}}\)d, B = 9 + 99 + 999 + .... + 9999...9 ( 50 chữ số 9...
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Tính :
a, \((\sqrt{2}-\sqrt{3}).\left(\sqrt{2}+\sqrt{3}\right)\)
b, \(-(\sqrt{2})^4+\left(\sqrt{3}\right)^6\)
c , \(A=\frac{1}{1-\frac{1}{1-2^{-4}}}+\frac{1}{1+\frac{1}{1+2^{-1}}}\)
d, B = 9 + 99 + 999 + .... + 9999...9
( 50 chữ số 9 )
a)
\((\sqrt2- \sqrt3).(\sqrt2+\sqrt3)\)
=\(\sqrt2.\sqrt2 + \sqrt2.\sqrt3-\sqrt3.\sqrt2+\sqrt3.\sqrt3\)
=\(1.1+1.\sqrt3-\sqrt3.1+\sqrt3.\sqrt3\)
=1+0+3=4
\(a,\left(\sqrt{2}-\sqrt{3}\right)\left(\sqrt{2}+\sqrt{3}\right)=\left(\sqrt{2}\right)^2-\left(\sqrt{3}\right)^2=2-3=-1\)
\(b,-\left(\sqrt{2}\right)^4+\left(\sqrt{3}\right)^6=-\left(\sqrt{2}^2\right)^2+\left(\sqrt{3}^2\right)^3=-2^2+3^3=-4+27=23\)
\(c,A=\frac{1}{1-\frac{1}{1-2^{-4}}}+\frac{1}{1+\frac{1}{1+2^{-1}}}=\frac{1}{1-\frac{1}{1-\frac{1}{16}}}+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}=\frac{1}{1-\frac{1}{\frac{15}{16}}}+\frac{1}{1+\frac{1}{\frac{3}{2}}}\)
\(=\frac{1}{1-\frac{16}{15}}+\frac{1}{1+\frac{2}{3}}=\frac{1}{-\frac{1}{15}}+\frac{1}{\frac{5}{3}}=-15+\frac{3}{5}=-14,4\)
\(d,B=9+99+...+99...9=\left(10-1\right)+\left(100-1\right)+...+\left(100...0-1\right)\)
\(=\left(10+100+...+100...0\right)-\left(1+1+...+1\right)=11...10-50=11...1060\)(có 48 chữ số 1)