Question

46.resuelve estas ecuaciones irracionales.
a. raiz 4x - 5x= -4x
b. 2 raiz x-5= 10-x
c.raiz x+5= x-1
d. 2x-2= raiz 8x-x
ayudenme por fiss

Answer 1

a) √ ( 4x ) - 5x = - 4x

√ 4x = - 4x + 5x

√4x = x

4x = x^2

x^2 + 4x = 0

x * (x + 4) = 0

x1 = 0  ;  x2 = - 4

b) 2 √ ( x - 5 ) = 10 - x

4 * ( x - 5 ) = ( 10 - x )^2

4x - 20 = 100 - 20x + x^2

x^2 - 20x - 4x + 100 + 20 = 0

x^2 - 24x + 120 = 0

x1,2 = { - (- 24) +/- √ [ (- 24)^2 - 4*(1) (120) ] } / 2(1)

x1,2 = { 24 +/- √ (96) } / 2

c) √ ( x - 5 ) = x - 1

(x - 5) = (x - 1)^2

x - 5 = x^2 - 2x + 1

x^2 - 2x - x + 5 + 1 = 0

x^2 - 3x + 6 = 0

x1,2 = { -( - 3) +/- √ [ (- 3)^2 - 4*(1)(6) ] } / (2)(1)

x1,2 = { 3 +/- √ ( - 15) } / 2 ⇒ raíz imaginaria

d) 2x - 2 = √ (8x - x)

[ 2 (x - 1) ]^2 = 7x

4 * (x^2 - 2x + 1) = 7x

4x^2 - 8x + 4 = 7x

4x^2 - 8x - 7x + 4 = 0

4x^2 - 15x + 4 = 0

x^2 - (15/4)x + 1 = 0

x1,2 = { - (- 15/4) +/- √ [ ( -15/4)^2 - 4*(1)(1) ] } / (2)

x1,2 = (15 / 4) +/- √ [ (225 / 16) - 4 ] } / 2

x1,2 = (15/4) +/- √ [ (225 - 64) / 16 ] / 2

x1,2 = (15/4) +/- √ (161 / 16) / 2

x1,2 = [ (15/4) +/- (1/4) √161 ] / 2

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Answer 2

a.4x −5x = −4x

4x =5x − 4x

4x = x → 4x = x2

x2 −4x = 0→x(x−4)= 0

x = 0,x = 4

b.2 x −5=10− x

2 x =10− x+5→ 2 x =15− x

x = (15− x)2 → 4x = 225− 30x+ x2

x2 − 30x − 4x+225= 0→ x2 − 34x+225= 0

(x−25)(x−9)= 0→ x = 9

c.x+15 = x −1

x+5= (x−1)2 → x+5= x2 − 2x+1

x2 − 2x+1− x −5= 0→ x2 − 3x − 4 = 0

(x+1)(x−4)= 0, → x = 4

d.2x − 2= 8x − x

2x+ x−2= 8x→(3x−2)2

= 8x

9x2 −12x+4 − 8x = 0

9x2 −20x+4 = 0→(9x−2)(x−2)= 0

x = 2