Question

resolver la siguiente ecuación irracional √4x-3-√x-2=2√x​

Answer 1

Respuesta:

√(4x-3) - √(x-2) = 2√x

√(4x-3) = 2√x + √(x-2)

(√(4x-3))^2 = (2√x+√(x-2))^2

4x-3 = (2√x+√(x-2))^2

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

4x-3 = (2)^2(√x)^2+(2×2)((√x)(√(x-2))+x-2

4x-3 = 4x+4√(x(x-2))+x-2

4x-3 = 5x+4√(x^2-2x)-2

4x-3+2 = 5x+4√(x^2-2x)-2+2

4x-1 = 5x+4√(x^2-2x)

4x-1-5x = 5x+4√(x^2-2x)-5x

-x-1 = 4√(x^2-2x)

-(x+1) = 4√(x^2-2x)

-(x+1)/-1 = 4√(x^2-2x)/-1

x+1 = -4√(x^2-2x)

(x+1)^2 = (-4√(x^2-2x)^2

x^2+2x+1 = (-4)^2(√(x^2-2x))^2

x^2+2x+1 = 16(x^2-2x)

x^2+2x+1 = 16x^2-32x

x^2+2x+1 +32x = 16x^2-32x+32x

x^2+(2+32)x+1 = 16x^2

x^2+34x+1 = 16x^2

x^2+34x+1-16x^2 = 16x^2-16x^2

(1-16)x^2+34x+1 = 0

-15x^2+34x+1 = 0

-1( -15x^2+34x+1 ) = -1(0)

15x^2- 34x- 1 = 0

x = -(-34)+-(√((-34)^2-4(15)(-1)/(2×15))

x = 34+-(√((1156+((-60)(-1))/30)

x = 34 +-((√(1156+60)/30)

x = 34+-(√(1216)/30) ; √1216 = 8√19

x = 34+-(8√19/30)

x = 34/30+-(8√19/30)

x = 17/5 +-4√19/15

x1 = (17+4√19)/15

x2 = (17-4√19)/15

Espero eso te sea útil.

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