Solve sqrt{1+a}=sqrt{4-2a}

$$\sqrt { 1 + a } = \sqrt { 4 - 2 a }$$

Solve for a

$$a=1$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{1+a}\right)^{2}=\left(\sqrt{4-2a}\right)^{2}$$

Calculate \sqrt{1+a} to the power of 2 and get 1+a.

$$1+a=\left(\sqrt{4-2a}\right)^{2}$$

Calculate \sqrt{4-2a} to the power of 2 and get 4-2a.

$$1+a=4-2a$$

Add 2a to both sides.

$$1+a+2a=4$$

Combine a and 2a to get 3a.

$$1+3a=4$$

Subtract 1 from both sides.

$$3a=4-1$$

Subtract 1 from 4 to get 3.

$$3a=3$$

Divide both sides by 3.

$$a=\frac{3}{3}$$

Divide 3 by 3 to get 1.

$$a=1$$

Substitute 1 for a in the equation \sqrt{1+a}=\sqrt{4-2a}.

$$\sqrt{1+1}=\sqrt{4-2}$$

Simplify. The value a=1 satisfies the equation.

$$2^{\frac{1}{2}}=2^{\frac{1}{2}}$$

Equation \sqrt{a+1}=\sqrt{4-2a} has a unique solution.

$$a=1$$