Solve for a
a=0
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\left(\sqrt{a}+\sqrt{a}\right)^{2}=\left(\sqrt{2a}\right)^{2}
Square both sides of the equation.
\left(2\sqrt{a}\right)^{2}=\left(\sqrt{2a}\right)^{2}
Combine \sqrt{a} and \sqrt{a} to get 2\sqrt{a}.
2^{2}\left(\sqrt{a}\right)^{2}=\left(\sqrt{2a}\right)^{2}
Expand \left(2\sqrt{a}\right)^{2}.
4\left(\sqrt{a}\right)^{2}=\left(\sqrt{2a}\right)^{2}
Calculate 2 to the power of 2 and get 4.
4a=\left(\sqrt{2a}\right)^{2}
Calculate \sqrt{a} to the power of 2 and get a.
4a=2a
Calculate \sqrt{2a} to the power of 2 and get 2a.
4a-2a=0
Subtract 2a from both sides.
2a=0
Combine 4a and -2a to get 2a.
a=0
Product of two numbers is equal to 0 if at least one of them is 0. Since 2 is not equal to 0, a must be equal to 0.
\sqrt{0}+\sqrt{0}=\sqrt{2\times 0}
Substitute 0 for a in the equation \sqrt{a}+\sqrt{a}=\sqrt{2a}.
0=0
Simplify. The value a=0 satisfies the equation.
a=0
Equation \sqrt{a}+\sqrt{a}=\sqrt{2a} has a unique solution.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}