4/7=8/...=.../21=16/...=20/35=.../70
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a) 7 x 5 = 35 7 x 6 = 42 7 x 8 = 56 7 x 4 = 28
35 : 7 = 5 42 : 7 = 6 56 : 7 = 8 28 : 7 = 4
b) 42 : 7 = 6 35 : 7 = 5 63 : 7 = 9 16 : 2 = 8
14 : 7 = 2 49 : 7 = 7 7 : 7 = 1 48 : 6 = 8
28 : 7 = 4 70 : =10 21 : 7 = 3 56 : 7 = 8
14) \(\sqrt{7-4\sqrt{3}}=2-\sqrt{3}\)
15) \(\sqrt{8+2\sqrt{15}}=\sqrt{5}+\sqrt{3}\)
16) \(\sqrt{10-2\sqrt{21}}=\sqrt{7}-\sqrt{3}\)
17) \(\sqrt{11+2\sqrt{18}}=3+\sqrt{2}\)
18) \(\sqrt{7+2\sqrt{10}}=\sqrt{5}+\sqrt{2}\)
19) \(\sqrt{7+4\sqrt{3}}=2+\sqrt{3}\)
20) \(\sqrt{12-2\sqrt{35}}=\sqrt{7}-\sqrt{5}\)
2-4+6-8+10-12+14-16+18-20+22
=(2+18)-(4+16)+(6+14)-(8+12)-(10+20)+22
=20-20+20-20-20+22
=22-20
=2
\(A=\frac{14^{16}-21^{32}.35^{68}}{10^{16}.15^2.7^{96}}=\frac{2^{16}.7^{16}-3^{32}.7^{32}.7^{68}.5^{68}}{5^{16}.2^{16}.3^2.5^2.7^{96}}\)
\(A=\frac{2^{16}.7^{16}-3^{32}.7^{100}.5^{68}}{5^{18}.2^{16}.3^2.7^{96}}=\frac{7^{16}.\left(2^{16}-3^{32}.7^{84}.5^{68}\right)}{5^{18}.2^{16}.3^2.7^{96}}=\frac{2^{16}-3^{32}.7^{84}.5^{68}}{5^{18}.2^{16}.3^2.7^{88}}\)
\(B=\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}=\frac{2^{40}-2^{20}+2^{20}.3^{20}}{2^{20}.3^{20}-3^{20}+3^{40}}=\frac{2^{20}.\left(2^{20}-1+3^{20}\right)}{3^{20}.\left(2^{20}-1+3^{20}\right)}\)
\(B=\frac{2^{20}}{3^{20}}\)
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37
=(1+37)x37:2
=703
\(\dfrac{4}{7}=\dfrac{8}{14}=\dfrac{12}{21}=\dfrac{16}{28}=\dfrac{20}{35}=\dfrac{40}{70}\)
4/7=8/14=12/21=16/28=20/35=40/70