Solve: 3 \sqrt { 4 x + 1 } + 4 x \sqrt { 3 x - 2 } = 3 x ^ { 2 } + 4 x + 5 ​

Question

Solve:
`3 \sqrt { 4 x + 1 } + 4 x \sqrt { 3 x - 2 } = 3 x ^ { 2 } + 4 x + 5`
​

Answer 1

The answer is that z=2

Answer 2

Explanation:

Solution

Multiply by 2

`\tt{} {6x}^(2) + 8x + 10 - 6 √(4x + 1) - 8x √(3x - 2) = 0`

`\tt{}\to\begin{pmatrix}3 - √(4x+1)\end{pmatrix}^(2)+4\begin{pmatrix}x-√(3x-2)\end{pmatrix}^(2)+2\begin{pmatrix}x - 2\end{pmatrix}^(2) = 0`

`\tt{} \to \begin{cases}x - 2 = 0 \\ 3 - √(4x + 1) = 0 \\x - √(3x - 2) = 0\end{cases}`

X = 2 satisfy the above system of equations

So, x = 2 is the unique solution.

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