Question

Solve √9+3x-✓2x=5/√9+2x (pls mention who the 16x came and tell why we need to multiply it with square)​

Answer 1

Answer:

8

Step-by-step explanation:

Given: The expression √(9 + 2x) - √(2x) = 5/√(9 + 2x)

To find: Solve for x.

Solution:

We have given the term:

             √(9 + 2x) - √(2x) = 5/√(9 + 2x)

Solving it further, we get:

            √(9 + 2x){√(9 + 2x) - √(2x)} = 5

            √(9 + 2x)² - {√(9 + 2x) × √(2x)} = 5

            9 + 2x - { √2x(9 + 2x) } = 5

            9 + 2x - √(18x + 4x²) = 5

            2x + 4 = √(18x + 4x²)

Now squaring on both sides, we get:

            (2x + 4)² = (18x + 4x²)

            4x² + 16 + 16x = 18x + 4x²

Cancelling 4x² from both sides, we get:

            16 + 16x = 18x

            16 = 2x

            x = 8

Answer:

        So the value of x is 8