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{ [ ( 2x + 19 ) : 22 - 3 ] : 2 } - 1 = 0
<=> [ ( 2x + 19 ) : 4 - 3 ] : 2 = 1
<=> [ ( 2x + 19 ) : 4 - 3 ] = 2
<=> ( 2x + 19 ) : 4 = 5
<=> 2x + 19 = 20
<=> 2x = 1
<=> x = 1/2
( P/s : ko chắc )
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200 - 5 [ ( 5^3 - 3^3 ) . 14 ]
= 200 - 5 [ 98.14]
= 200 - 5 . 1372
= 200 - 6860
= -6660
7^5 : 7^3 + 15 ( 2^3 . 15 - 5.4)
= 49 + 15 ( 8 . 15 - 20 )
= 49 + 15. 100
= 49 + 1500
= 1549
200-5[(53-33).14]=200-5[(125-27).14]=200-5(98.14)=200-5.1372=200-6860=-6660
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(315. 4 + 5. 315):316
=[315. (4+5)]:316
=[315. 9]: 316
=[315. 32]:316
=\(\frac{3^{15}.3^2}{3^{16}}=\frac{3^2}{3}=\frac{9}{3}=3\)
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Xét tỉ số \(\frac{3^{15}+4^{15}}{5^{15}}=\left(\frac{3}{5}\right)^{15}+\left(\frac{4}{5}\right)^{15}\)
Nhận xét:
+) \(\frac{3}{5}<1\) => \(\frac{3}{5}.\frac{3}{5}<1.\frac{3}{5}\) hay \(\left(\frac{3}{5}\right)^2<\frac{3}{5}\)=> \(\left(\frac{3}{5}\right)^3<\left(\frac{3}{5}\right)^2\).
tiếp tục nhân 2 vế với 3/5 ta có: \(\left(\frac{3}{5}\right)^{15}<\left(\frac{3}{5}\right)^{14}<...<\left(\frac{3}{5}\right)^3<\left(\frac{3}{5}\right)^2\)
Vậy \(\left(\frac{3}{5}\right)^{15}<\left(\frac{3}{5}\right)^2\)
+) Tương tự, \(\frac{4}{5}<1\) => \(\left(\frac{4}{5}\right)^{15}<\left(\frac{4}{5}\right)^{14}<...<\left(\frac{4}{5}\right)^3<\left(\frac{4}{5}\right)^2\)
Vậy \(\left(\frac{4}{5}\right)^{15}<\left(\frac{4}{5}\right)^2\)
=> \(\left(\frac{3}{5}\right)^{15}+\left(\frac{4}{5}\right)^{15}<\left(\frac{3}{5}\right)^2+\left(\frac{4}{5}\right)^2\) => \(\frac{3^{15}+4^{15}}{5^{15}}<\frac{25}{25}=1\)
=> 315 + 415 < 515
Vậy..............
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3 ^ 15= [ 3^3] ^5= 27 ^5 => 3^15 + 4^15 = 91^5
4^15= [ 4^3]^5 = 64 ^5 =>
5^15= [ 5^3]^5 = 125 ^5
125^5 > 91^5=> 3^15+4^15 < 5^15
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tìm số tự nhiên x biết
a, 2x - 15 =17
=> 2x = 17 + 15 = 32
=> 2x = 25
=> x = 5
b, ( 7x - 11)3 = 25 x 52+200
=> ( 7x - 11 )3 = 32 . 25 + 200
=> ( 7x - 11 )3 = 1000
=> ( 7x - 11 )3 = 103
=> 7x - 11 = 10
=> 7x = 10 + 11 = 21
=> x = 21 : 7 = 3
(2x-15)5=(2x-15)3
=> 2x-15=0 hoặc 2x-15=1 (vì 05=03)
=> 2x=0+15 hoặc 2x=1+15
=> 2x=15 hoặc 2x=16
=> x=15:2 hoặc x=16:2
=> x=7,5 hoặc x=8
Vậy x = 7,5 hoặc x = 8