Final answer:
To find the value of x in the equation (x√2-4√5x)²=0, we expand the square of a binomial and set it equal to zero. By factoring out a common term and solving for x, we find that the value of x is x = 41/2√10. The correct option is A .
Step-by-step explanation:
To find the value of x, we need to solve the equation (x√2-4√5x)²=0.
First, we expand the square of a binomial:
(x√2-4√5x)(x√2-4√5x) = x²(√2)² - 2(x√2)(4√5x) + (4√5x)²
= 2x² - 2(2√10x²) + (16)(5x²)
= 2x² - 4√10x² + 80x²
= 2x² - 4√10x² + 80x².
Next, we set the equation equal to zero:
2x² - 4√10x² + 80x² = 0
86x² - 4√10x² = 0
82x² - 4√10x²=0.
This equation can be simplified by factoring out a common term:
2x²(41 - 2√10) = 0.
To find the value of x, we set each factor equal to zero:
2x² = 0 (This gives us x = 0)
41 - 2√10 = 0 (This gives us √10 = 41/2)
Since we can't solve for x directly, we can approximate the value of √10 using a calculator:
√10 ≈ 3.16227766.
Then, we solve for x:
√10 = 41/2
x = 41/2√10.
Therefore, the value of x is x = 41/2√10. Answer choice B) x = 41/2√10.