Question

Rezolvati in R ecuatiile:
Va rog e urgent ,si va rog cu rezolvare completa.​

Answer 1

Răspuns:

Explicație pas cu pas:

Toate ecuatiile sunt ecuatii de gradul 2

ax^2 + bx + c = 0

Δ = b^2 - 4a*c

x1 = (-b + √Δ)/2a

x2 = (-b - √Δ)/2

_____________

4a)

x^2 - 7x + 6 = 0

Δ = 49 - 24 = 25

x1 = (7 + 5)/2 = 6

x2 = (7 - 5)/2 = 1

________________

5a)

x^2 - 5x + 6 = 0

Δ = 25 - 24 = 1

x1 = (5 + 1)/2 = 3

x2 = (5 - 1)/2 = 2

_________________

6a)

2x^2 + x - 3 = 0

Δ = 1 + 24 = 25

x1 = (-1 + 5)/4 = 1

x2 = (-1 - 5)/4 = -6/4 = -3/2

____________________

Spor la treaba!

Answer 2

Răspuns:

4)

a)x²-7x+6=0

x²-x-6x+6=0

x(x-1)-6(x-1)=0

(x-1)(x-6)=0

x-1=0

x-1+1=0+1

x=0+1

x=1

x-6=0

x-6+6=0+6

x=0+6

x=6

S={1,6}

b)x²+2x-8=0

x²+4x-2x-8=0

x(x+4)-2(x+4)=0

(x+4)(x-2)=0

x+4=0

x+4-4=0-4

x=0-4

x=-4

x-2=0

x-2+2=0+2

x=0+2

x=2

S={-4,2}

c)x²+5x-14=0

x²+7x-2x-14=0

x(x+7)-2(x+7)=0

(x+7)(x-2)=0

x+7=0

x+7-7=0-7

x=0-7

x=-7

x-2=0

x-2+2=0+2

x=0+2

x=2

S={-7,2}

d)x²-8x-20=0

x²+2x-10x-20=0

x(x+2)-10(x+2)=0

(x+2)(x-10)=0

x+2=0

x+2-2=0-2

x=0-2

x=-2

x-10=0

x-10+10=0+10

x=0+10

x=10

S={-2,10}

e)x²+4x-12=0

x²+6x-2x-12=0

x(x+6)-2(x+6)=0

(x+6)(x-2)=0

x+6=0

x+6-6=0-6

x=0-6

x=-6

x-2=0

x-2+2=0+2

x=0+2

x=2

S={-6,2}

f)x²-7x-30=0

x²+3x-10x-30=0

x(x+3)-10(x+3)=0

(x+3)(x-10)=0

x+3=0

x+3-3=0-3

x=0-3

x=-3

x-10=0

x-10+10=0+10

x=0+10

x=10

S={-3,10}

g)x²-9x+14=0

x²-2x-7x+14=0

x(x-2)-7(x-2)=0

(x-2)(x-7)=0

x-2=0

x-2+2=0+2

x=0+2

x=2

x-7=0

x-7+7=0+7

x=0+7

x=7

S={2,7}

h)x²-10x+16=0

x²-2x-8x+16=0

x(x-2)-8(x-2)=0

(x-2)(x-8)=0

x-2=0

x-2+2=0+2

x=0+2

x=2

x-8=0

x-8+8=0+8

x=0+8

x=8

S={2,8}

i)x²+7x+10=0

x²+5x+2x+10=0

x(x+5)+2(x+5)=0

(x+5)(x+2)=0

x+5=0

x+5-5=0-5

x=0-5

x=-5

x+2=0

x+2-2=0-2

x=0-2

x=-2

S={-5,-2}

5)

a)x²-5x+6=0

x²-2x-3x+6=0

x(x-2)-3(x-2)=0

(x-2)(x-3)=0

x-2=0

x-2+2=0+2

x=0+2

x=2

x-3=0

x-3+3=0+3

x=0+3

x=3

S={2,3}

b)x²+x-6=0

x²+3x-2x-6=0

x(x+3)-2(x+3)=0

(x+3)(x-2)=0

x+3=0

x+3-3=0-3

x=0-3

x=-3

x-2=0

x-2+2=0+2

x=0+2

x=2

S={-3,2}

c)x²-7x+12=0

x²-3x-4x+12=0

x(x-3)-4(x-3)=0

(x-3)(x-4)=0

x-3=0

x-3+3=0+3

x=0+3

x=3

x-4=0

x-4+4=0+4

x=0+4

x=4

S={3,4}

d)x²+x-12=0

x²+4x-3x-12=0

x(x+4)-3(x+4)=0

(x+4)(x-3)=0

x+4=0

x+4-4=0-4

x=0-4

x=-4

x-3=0

x-3+3=0+3

x=0+3

x=3

S={-4,3}

e)x²-6x+8=0

x²-2x-4x+8=0

x(x-2)-4(x-2)=0

(x-2)(x-4)=0

x-2=0

x-2+2=0+2

x=0+2

x=2

x-4=0

x-4+4=0+4

x=0+4

x=4

S={2,4}

f)x²+3x-10=0

x²+5x-2x-10=0

x(x+5)-2(x+5)=0

(x+5)(x-2)=0

x+5=0

x+5-5=0-5

x=0-5

x=-5

x-2=0

x-2+2=0+2

x=0+2

x=2

S={-5,2}

g)x²-8x+15=0

x²-3x-5x+15=0

x(x-3)-5(x-3)=0

(x-3)(x-5)=0

x-3=0

x-3+3=0+3

x=0+3

x=3

x-5=0

x-5+5=0+5

x=0+5

x=5

S={3,5}

h)x²+2x-24=0

x²+6x-4x-24=0

x(x+6)-4(x+6)=0

(x+6)(x-4)=0

x+6=0

x+6-6=0-6

x=0-6

x=-6

x-4=0

x-4+4=0+4

x=0+4

x=4

S={-6,4}

i)x²-4x-21=0

x²+3x-7x-21=0

x(x+3)-7(x+3)=0

(x+3)(x-7)=0

x+3=0

x+3-3=0-3

x=0-3

x=-3

x-7=0

x-7+7=0+7

x=0+7

x=7

S={-3,7}

6)

a)2x²+x-3=0

2x²+3x-2x-3=0

x(2x+3)-(2x+3)=0

(2x+3)(x-1)=0

2x+3=0

2x+3-3=0-3

2x=0-3

2x=-3

2x:2=-3:2

x=-3:2

$x = - \frac{3}{2}$

x-1=0

x-1+1=0+1

x=0+1

x=1

S={$- \frac{3}{2}$,1}

b)2x²-x-15=0

2x²+5x-6x-15=0

x(2x+5)-3(2x+5)=0

(2x+5)(x-3)=0

2x+5=0

2x+5-5=0-5

2x=0-5

2x=-5

2x:2=-5:2

x=-5:2

$x = - \frac{5}{2}$

x-3=0

x-3+3=0+3

x=0+3

x=3

S={$- \frac{5}{2}$,3}

c)3x²-5x+2=0

3x²-2x-3x+2=0

x(3x-2)-(3x-2)=0

(3x-2)(x-1)=0

3x-2=0

3x-2+2=0+2

3x=0+2

3x=2

3x:3=2:3

x=2:3

$x = \frac{2}{3}$

x-1=0

x-1+1=0+1

x=0+1

x=1

S={$\frac{2}{3}$,1}

d)2x²-5x+2=0

2x²-x-4x+2=0

x(2x-1)-2(2x-1)=0

(2x-1)(x-2)=0

2x-1=0

2x-1+1=0+1

2x=0+1

2x=1

2x:2=1:2

x=1:2

$x = \frac{1}{2}$

x-2=0

x-2+2=0+2

x=0+2

x=2

S={$\frac{1}{2}$,2}

e)2x²+3x+1=0

2x²+2x+x+1=0

2x(x+1)+x+1=0

(x+1)(2x+1)=0

x+1=0

x+1-1=0-1

x=0-1

x=-1

2x+1=0

2x+1-1=0-1

2x=0-1

2x=-1

2x:2=-1:2

x=-1:2

$x = - \frac{1}{2}$

S={-1,$- \frac{1}{2}$}

f)2x²-x-3=0

2x²+2x-3x-3=0

2x(x+1)-3(x+1)=0

(x+1)(2x-3)=0

x+1=0

x+1-1=0-1

x=0-1

x=-1

2x-3=0

2x-3+3=0+3

2x=0+3

2x=3

2x:2=3:2

x=3:2

$x = \frac{3}{2}$

S={-1,$\frac{3}{2}$}

g)3x²+x-2=0

3x²+3x-2x-2=0

3x(x+1)-2(x+1)=0

(x+1)(3x-2)=0

x+1=0

x+1-1=0-1

x=0-1

x=-1

3x-2=0

3x-2+2=0+2

3x=0+2

3x=2

3x:3=2:3

x=2:3

$x = \frac{2}{3}$

S={-1,$\frac{2}{3}$}

h)3x²+4x-7=0

3x²+7x-3x-7=0

x(3x+7)-(3x+7)=0

(3x+7)(x-1)=0

3x+7=0

3x+7-7=0-7

3x=0-7

3x=-7

3x:3=-7:3

x=-7:3

$x = - \frac{7}{3}$

x-1=0

x-1+1=0+1

x=0+1

x=1

S={$- \frac{7}{3}$,1}

i)2x²+x-1=0

2x²+2x-x-1=0

2x(x+1)-(x+1)=0

(x+1)(2x-1)=0

x+1=0

x+1-1=0-1

x=0-1

x=-1

2x-1=0

2x-1+1=0+1

2x=0+1

2x=1

2x:2=1:2

x=1:2

$x = \frac{1}{2}$

S={-1,$\frac{1}{2}$}