Question

a)(x+4)²=36
b)(x-4)²=49
c)(x+2)²=70
d)(x+4)²=49
e)(x-3)²=36
f)(x-3)²+3=28
g)(x+4)²+7=56
h)(x-3)²-5=37
i)(x+8)²+54=-27
alguien que me ayude, por favor​

Answer 1

Respuesta:

a) x= -10       x =2

b) x = - 11           x=3

c)  x = 5,874       x= -9,88

d) x= -11       x= 6

e) x= -3        x=9

f) x= -2       x= 8

g) x= - 11          x= 3

h) x=24,48           x=11,52

i)x= -17           x= 1

Explicación paso a paso:

a) (x+4)² = 36

x² + 2 (x) (4) + 4² = 36

x² + 8x + 16 = 36

x² + 8x + 16 - 36 = 0

x² + 8x -20 = 0

( x + 10  ) ( x - 2) = 0

x+10 = 0          

x = -10  

x - 2 = 0

x = 2

otra manera de realizarlo

(x+4)² = 36

(x+4)² - 36 = 0

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

(x +10) ( x + 4 -6) = 0

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

x+10 = 0

x = -10

x - 2 = 0

x = 2

b) (x+4)² = 49

x² + 2 (x) (4) + 4² = 49

x² + 8x + 16 = 49

x² + 8x + 16 - 49 = 0

x² + 8x - 33 = 0

(x + 11  ) ( x -  3 )= 0

x+11 = 0

x = - 11

x - 3 = 0

x = 3

(x+4)² = 49

(x+4)² - 49 = 0

(x+4 +7) (x+4 -7) = 0

(x+11) (x-3) = 0

x+11 = 0

x = - 11

x-3 = 0

x= 3

c) (x+2)² = 70

x²+ 2 (x) (2) + 2² = 70

x² + 4x + 4 - 70 = 0

x² +  4x - 66 = 0

sacamos con la formula general  x = (-b ± $\sqrt{b^{2} } -4ac$) / 2a

x= ( - 4 ± $\sqrt{4^{2} - 4(1)(66) }$ ) / 2(1)

x= (-4 ± $\sqrt{4^{2} -4 (1)(66) }$ ) / 2

x= (- 4 ± $\sqrt{16-264}) / 2$

x = ( -4 ± $\sqrt{248} ) /2$

x = (-4 ±$2\sqrt{62} )$ / 2

x= 2( -2 ± √62) / 2

x = -2 ± √62

x= -2 + √62

x = 5,874

x = - 2 - √62

x= - 9,88

d) (x+4)² = 49

(x+4)² - 49 = 0

(x+4+7) (x+4-10) =

(x + 11) ( x - 6)= 0

x+11 = 0

x = -11

x - 6 = 0

x = 6

e) (x-3)² = 36

(x-3)² - 36 = 0

(x-3 +6 )(x -3 -6) = 0

(x+3) ( x - 9) = 0

x+3 = 0

x = - 3

x - 9 = 0

x = 9

f) (x-3)² +3 = 28

(x-3)² +3 -28 = 0

(x-3)² -25 = 0

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

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

x+2 = 0

x = -2

x - 8 = 0

x = 8

g) (x+4)² +7 = 56

(x+4)² + 7 - 56 = 0

(x+4)² - 49 = 0

(x + 4 +7 ) (x+4 -7) = 0

(x + 11) ( x -3 ) = 0

x + 11 = 0

x = - 11

x - 3 = 0

x = 3

h) (x-3)² -5 = 37

(x-3)² - 5 -37 = 0

(x-3)² - 42 = 0

x² - 6x +9 -42 = 0

x² - 6x -33 = 0

sacamos con la formula general  x = (-b ± $\sqrt{b^{2} } -4ac$) / 2a

x= ( - (-6)) ± $\sqrt{-6^{2} - 4(1)(-33) }$ ) / 2(1)

x= ( 36 ± $\sqrt{36 +132}$) / 2

x= (36 ± $\sqrt{168} )/2$

x = (36 + $\sqrt{168} ) /2$

x= 24,48

x= (36 - $\sqrt{168} )/2$

x= 11,52

i) (x+8)² +54 = -27

(x+8)² +54 +27 = 0

(x+8)² +81 = 0

(x+8 +9) (x+8 -9) = 0

(x + 17 ) (x - 1) = 0

x+17 = 0

x= -17

x-1 = 0

x = 1