Question

[Thái]

Câu 1:

A = -7⁴⁹ - {-223 - [ -123 - (200 - 7⁴⁹) + 2023 ]}

B = 1.2 + 2.3 + 3.4 + ... + 80.81

C = \(\dfrac{2^{12}.9^4-3^9.8^4}{2^{13}.2^8-8^4.27^3}\)

Câu 2:

Tìm số nguyên x biết : 3 . 49^x = 35 . 7²⁰²³ - 14 . 7²⁰²³

Câu 3:

Tìm số nguyên tố p sao cho p+6; p+12; p+18; p+24 cũng là các số nguyên tố

Answer 1

[Akai Haruma]

Câu 1:

\(A=-7^{49}-\left\{-223-[-123-(200-7^{49})+2023]\right\}\)

\(=-7^{49}+223+[-123-(200-7^{49})+2023]\)

\(=-7^{49}+223-123-(200-7^{49})+2023\)

\(=-7^{49}+(223-123)-200+7^{49}+2023\)

$=(-7^{49}+7^{49})+(223-123)-200+2023$

$=0+100-200+2023=2023-100=1923$

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$3B=1.2.3+2.3.3+3.4.3+....+80.81.3$

$3B=1.2.3+2.3(4-1)+3.4(5-2)+...+80.81(82-79)$

$3B=1.2.3+2.3.4+3.4.5+...+80.81.82-(1.2.3+2.3.4+...+79.80.81)$

$3B=80.81.82$
$\Rightarrow B=\frac{80.81.82}{3}$

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\(C=\frac{2^{12}.(3^2)^4-3^9.(2^3)^4}{2^{13}.2^8-(2^3)^4.(3^3)^3}=\frac{2^{12}.3^8-3^9.2^{12}}{2^{21}-2^{12}.3^9}\)

\(=\frac{2^{12}.3^8(1-3)}{2^{12}(2^9-3^9)}=\frac{-2.3^8}{2^9-3^9}=\frac{2.3^8}{3^9-2^9}\)

Answer 2

[Akai Haruma]

Câu 2:

$3.49^x=35.7^{2023}-14.7^{2023}$

$3.(7^2)^x=5.7.7^{2023}-2.7.7^{2023}$

$3.7^{2x}=5.7^{2024}-2.7^{2024}=7^{2024}(5-2)=3.7^{2024}$

$\Rightarrow 7^{2x}=7^{2024}$

$\Rightarrow 2x=2024$
$\Rightarrow x=1012$