What is the answer to sqrt(2x)+sqrt(4x-7)=x+1 ?

The answer to sqrt(2x)+sqrt(4x-7)=x+1 is x=8,x=2

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sqrt(2x)+sqrt(4x-7)=x+1

2 x + 4 x - 7 = x + 1

x = 8, x = 2

Solution steps

2 x + 4 x - 7 = x + 1

Remove square roots

16 x^{3} + 4 x^{2} - 40 x - 28 = x^{4} + 8 x^{3} + 4 x^{2} - 48 x + 36

Switch sides

x^{2} + 6 x - 2 4 x - 7 x - 2 4 x - 7 - 6 = 2 x

Move

x^{2}

to the right side

6 x - 2 4 x - 7 x - 2 4 x - 7 - 6 = 2 x - x^{2}

Move

6 x

to the right side

- 2 4 x - 7 x - 2 4 x - 7 - 6 = - x^{2} - 4 x

Move

6

to the right side

- 2 4 x - 7 x - 2 4 x - 7 = - x^{2} - 4 x + 6

Factor

- 2 4 x - 7 x - 2 4 x - 7 : - 2 4 x - 7 (x + 1)

- 2 4 x - 7 (x + 1) = - x^{2} - 4 x + 6

Solve

16 x^{3} + 4 x^{2} - 40 x - 28 = x^{4} + 8 x^{3} + 4 x^{2} - 48 x + 36 : x = 8, x = 2

x = 8, x = 2

Verify Solutions:

x = 8

True

, x = 2

True

The solutions are

x = 8, x = 2

- 5 u + 1 + u + 4 = 3

2 = - 3 - x

x + 2 - x - 6 - 2 = 0

x + x + 1 = 2 x + 1

f, f^{- 1} (2) = 22 - 18 x

What is the answer to sqrt(2x)+sqrt(4x-7)=x+1 ?
The answer to sqrt(2x)+sqrt(4x-7)=x+1 is x=8,x=2
Solve for x: sqrt(2x)+sqrt(4x-7)=x+1
The solution is x=8,x=2