What is (sqrt(x+1)+sqrt(x))^2 ?

The solution to (sqrt(x+1)+sqrt(x))^2 is 2x+2sqrt(x)sqrt(x+1)+1

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simplify (sqrt(x+1)+sqrt(x))^2

simplify

(x + 1 + x)^{2}

2 x + 2 x x + 1 + 1

Solution steps

(x + 1 + x)^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(x + 1 + x)^{2} = (x + 1)^{2} + 2 x + 1 x + (x)^{2}

= (x + 1)^{2} + 2 x + 1 x + (x)^{2}

Simplify

(x + 1)^{2} + 2 x + 1 x + (x)^{2} : 2 x + 2 x x + 1 + 1

= 2 x + 2 x x + 1 + 1

(x + \frac{( 1 + 5 )}{2}) (x + \frac{( 1 - 5 )}{2})

(4 - x) ln (x + 4)

ln (x) (e^{x} v_{1} + \frac{e ^{x}}{x} v_{2} = 0)

(- 2 y + 8 + 2)^{2}

(4 y - 5 i)^{2}

What is (sqrt(x+1)+sqrt(x))^2 ?
The solution to (sqrt(x+1)+sqrt(x))^2 is 2x+2sqrt(x)sqrt(x+1)+1