Question

va roggg urgentttttttt cat de repede​

Answer 1

Răspuns:

Explicație pas cu pas:

a) √(x + 1) = 2

Conditia de existenta a radicalului: x + 1 ≥ 0; x ≥ -1

√(x + 1) = 2 ridicam la patrat

x + 1 = 4

x = 3

Solutia x = 3

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b) √(x - 3) = x - 3

Conditia de existenta a radicalului x - 3 ≥ 0; x ≥ 3

√(x - 3) = x - 3 ridicam la patrat

x - 3 = (x - 3)^2

x - 3 = x^2 -6x + 9

x^2 - 6x - x + 9 + 3 = 0

x^2 - 7x + 12 = 0

Δ = 49 - 4*12 = 49 - 48 = 1

x1 = (7 + 1)/2 = 4

x2 = (7 - 1)/2 = 3

Solutie x = {3, 4}

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f) √(7 - x) + √(x - 5) = √2

7 -x ≥ 0 ;  x - 5 ≥ 0

x ≤ 7 ;

x ≤ 5; deci x ≤ 7

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√(7 - x) + √(x - 5) = √2 ridicam la patrat

7 - x + x - 5 + 2√(7 - x)(x - 5) = 2

2√(7 - x)(x - 5) = 0

(7 - x)(x - 5) = 0

x = 7 si x = 5

solutia x = {5, 7}

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h) √(1 + 2x) + √(4 - x) = 3

1 + 2x ≥ 0; 4 - x ≥ 0

x ≥ -1/2; x ≤ 4

-1/2 ≤ x ≤ 4

√(1 + 2x) + √(4 - x) = 3 ridicam la patrat

1 + 2x + 4 - x + 2√(1 + 2x)(4 - x) = 9

5 + x +  2√(1 + 2x)(4 - x) - 9 = 0

x + 2√(1 + 2x)(4 - x) - 4 = 0

2√(1 + 2x)(4 - x) = 4 - x

4(1 + 2x)(3 - x) = (4 - x)^2

4(3 - x + 6x -2x^2) = 16 - 8x + x^2

12 + 20x - 8x^2 = 16 - 8x + x^2

9x^2 - 28x + 4 = 0

Δ = 784 - 144 = 640

x1 = (28 + 8√10)/2 = 14 + 4√10 nu apartine intervalului de existenta pentru radicali

x2 = 14 - 4√10 apartine intervalului de existenta pentru radicali

Solutia x = 14-4√10

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g) √2x + √(6-x) = 4

x ≥ 0; 6 - x ≥0

0 ≤ x ≤ 6

2x + 6 - x + 2√2x(6 - x) = 16

x + 6 + 2√2x(6 - x) = 16

2√2x(6 - x) = 10 - x

4[2x(6 - x)] = 100 + x^2 - 2x

4(12x - 2x^2) = 100 + x^2 - 2x

48x - 8x^2 = 100 + x^2 - 2x

9x^2 - 50x + 100 = 0

Δ = 2500 - 4*100*9 = 2500 - 3600 = -1100

ecuatia nu are solutii reale