Question

Find the values of x for which √x - 2squqre root of x+5 =8 using radical equation method

Answer 1

To solve the given equation using the radical equation method, we will isolate the radical term on one side of the equation and then square both sides to eliminate the square root.

Given equation: √x - 2√(x+5) = 8

Add 2√(x+5) to both sides:
√x = 2√(x+5) + 8

Square both sides:
(√x)^2 = (2√(x+5) + 8)^2
x = 4(x+5) + 16 + 16√(x+5)
x = 4x + 20 + 16 + 16√(x+5)
3x = 36 + 16√(x+5)

Now, isolate the radical term and square both sides again:

3x - 36 = 16√(x+5)
(3x - 36)^2 = (16√(x+5))^2
9x^2 - 216x + 1296 = 256(x+5)
9x^2 - 216x + 1296 = 256x + 1280
9x^2 - 472x + 16 = 0

Now, we have a quadratic equation to solve:
9x^2 - 472x + 16 = 0

Using the quadratic formula:
x = [472 ± √(472^2 - 4*9*16)] / 18
x = [472 ± √(222784 - 576)] / 18
x = [472 ± √222208] / 18
x = [472 ± 471.077] / 18
x = (472 + 471.077) / 18 or x = (472 - 471.077) / 18
x = 943.077 / 18 or x = 0.923 / 18
x ≈ 52.393 or x ≈ 0.051

Therefore, the values of x for which the given equation holds true are approximately 52.393 and 0.051.