Solve sqrt{13-10t}=sqrt{11-11t}

$$\sqrt { 13 - 10 t } = \sqrt { 11 - 11 t }$$

Solve for t

$$t=-2$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{13-10t}\right)^{2}=\left(\sqrt{11-11t}\right)^{2}$$

Calculate \sqrt{13-10t} to the power of 2 and get 13-10t.

$$13-10t=\left(\sqrt{11-11t}\right)^{2}$$

Calculate \sqrt{11-11t} to the power of 2 and get 11-11t.

$$13-10t=11-11t$$

Add 11t to both sides.

$$13-10t+11t=11$$

Combine -10t and 11t to get t.

$$13+t=11$$

Subtract 13 from both sides.

$$t=11-13$$

Subtract 13 from 11 to get -2.

$$t=-2$$

Substitute -2 for t in the equation \sqrt{13-10t}=\sqrt{11-11t}.

$$\sqrt{13-10\left(-2\right)}=\sqrt{11-11\left(-2\right)}$$

Simplify. The value t=-2 satisfies the equation.

$$33^{\frac{1}{2}}=33^{\frac{1}{2}}$$

Equation \sqrt{13-10t}=\sqrt{11-11t} has a unique solution.

$$t=-2$$