What is the inverse of (x^2+5x)^{1/2} ?

The inverse of (x^2+5x)^{1/2} is (-5+(25+4x^2)^{1/2})/2 ,(-5-(25+4x^2)^{1/2})/2

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inverse of (x^2+5x)^{1/2}

inverse

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

\frac{- 5 + ( 25 + 4 x ^{2} ) ^{\frac{1}{2}}}{2}, \frac{- 5 - ( 25 + 4 x ^{2} ) ^{\frac{1}{2}}}{2}

Solution steps

y = (x^{2} + 5 x)^{\frac{1}{2}}

Replace

x

with

y

x = (y^{2} + 5 y)^{\frac{1}{2}}

Solve for

y, x = (y^{2} + 5 y)^{\frac{1}{2}}

\frac{- 5 + ( 25 + 4 x ^{2} ) ^{\frac{1}{2}}}{2}, \frac{- 5 - ( 25 + 4 x ^{2} ) ^{\frac{1}{2}}}{2}

What is the inverse of (x^2+5x)^{1/2} ?
The inverse of (x^2+5x)^{1/2} is (-5+(25+4x^2)^{1/2})/2 ,(-5-(25+4x^2)^{1/2})/2