Question

(2x-y)2+4x(x+y)2x= √2 y=√7

Answer 1

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Answer 2

To solve the given equation (2x-y)^(2) + 4x(x+y)^(2x) = √2, with y = √7, we can substitute the value of y into the equation and then solve for x.

Let's start by substituting y = √7 into the equation:

(2x - √7)^(2) + 4x(x + √7)^(2x) = √2

Now we can simplify the equation:

(2x - √7)^(2) + 4x(x + √7)^(2x) - √2 = 0

Expanding the squared terms:

(4x^(2) - 4√7x + 7) + 4x(x + √7)^(2x) - √2 = 0

Rearranging the equation:

4x^(2) + 4x(x + √7)^(2x) - 4√7x + 7 - √2 = 0

Now we have a quadratic equation in terms of x. We can solve it by factoring, completing the square, or using the quadratic formula. However, it's important to note that the equation might not have a simple algebraic solution and could require numerical methods to find an approximate solution.

If you need further assistance with solving the equation or any other questions, please let me know!