Question

19 si 20‼️ urgent dau coroana❗️

Answer 1

Răspuns:

Explicație pas cu pas:

19)

a) 4⁵+4⁸-4⁴ = 4⁴·(4+4⁴-1) = 4⁴·(4+256-1) = 4⁴·259 = 4⁴·7·37

b) 3³+6⁵+3⁴ = 3³·(1+3²·2³+3) = 3³·(1+72+3) = 3³·76 = 27·76

c) x²+x³+x⁴ = x²·(1+x+x²)

d) 5³·6+5⁴·7 = 5³·(6+5·7) = 5³·(6+35) = 5³·41

e)3x²y+2xy²+4xy = xy·(3x+2y+4)

f) 7⁵·x + 7⁴·y + 49z = 49·(7³x+7²y+z) = 49·(343x + 49y +z)

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20)

a) 3ˣ +3ˣ⁻¹ = 4  <=> 3·3ˣ⁻¹ + 3ˣ⁻¹ = 4 <=>

3ˣ⁻¹·(3+1) = 4 <=> 3ˣ⁻¹ = 4:4 = 1 = 3⁰  =>

x-1 = 0 => x = 1

b) 3ˣ+3ˣ⁻¹+3ˣ⁻²+3ˣ⁻³ = 40 <=>

3ˣ⁻³·(3³+3²+3+1) = 40 <=> 3ˣ⁻³·(27+9+3+1) = 40 <=>

3ˣ⁻³ ·40 = 40  => 3ˣ⁻³ = 40:40 = 1 = 3° =>

x-3 = 0 => x = 3

c) 5·3ˣ-2·3ˣ = 81 <=> 3ˣ·(5-2) = 81  =>

3·3ˣ = 81 => 3ˣ = 81:3 = 27 = 3³  => x = 3

d) 3²ˣ⁺¹-3²ˣ-3²ˣ⁻¹-3²ˣ⁻²-3²ˣ⁻³ = 123 <=>

3²ˣ⁻³·(3⁴-3³-3²-3-1) = 123 =>

3²ˣ⁻³·(81-27-9-4) = 123 =>

3²ˣ⁻³·41 = 123 =>

3²ˣ⁻³ = 123:41 = 3 = 3¹ =>

2x-3 = 1 => 2x = 4 => x = 2