Solve each equation a x2 3x 5x b x3 3x2 2x 6 0 c x12

Solve each equation a) |x^2 - 3x| = 5x b) x^3 + 3x^2 - 2x - 6 = 0 c) x^1/2 + 3x^1/4 - 10 = 0 d) squareroot x + 4 + squareroot x - 1 = 5

Solution

Solution:-

a)

Here;

|x^2 - 3x| = 5x

=> x^2 - 3x = 5x and x^2 -3x = -5x

=> x^2 = 8x and x^2 = -2x

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

=> x = 0,8,-2

b)

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

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

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

=> x = 2,-2,-3

c)

x^1/2 +3x^1/4 -10 = 0

Let x^1/4 = t

=> t^2 +3t -10 =0

=> t^2-2t+5t-10 =0

=> t(t-2)+5(t-2) = 0

=> (t-2)(t+5) = 0

=> t =2,-5

=> x^1/4 = 2,-5

=> x = 16,625

d)

Sqrt(x+4) = 5 - Sqrt(x-1)
x + 4 = 25 - 5*Sqrt(x-1) - 5*Sqrt(x-1) + (x-1)
x + 4 = 25 - 10*Sqrt(x-1) + x - 1
x + 4 = 25 - 1 + x - 10Sqrt(x-1)
x + 4 = 24 + x - 10Sqrt(x-1)
x - x + 4 - 24 = -10Sqrt(x-1)
-20 = -10Sqrt(x-1)
Square both sides -
+400 = +100(x-1)
400 = 100x - 100
400 + 100 = 100x
500 = 100x
5 = x