[Math] Solve equations $\sqrt{t +9} – \sqrt{t} = 1$

algebra-precalculusradicals

Solve equation: $\sqrt{t +9} – \sqrt{t} = 1$

I moved – √t to the left side of the equation $\sqrt{t +9} = 1 -\sqrt{t}$

I squared both sides $(\sqrt{t+9})^2 = (1)^2 (\sqrt{t})^2$

Then I got $t + 9 = 1+ t$

Can't figure it out after that point.

The answer is $16$

Best Answer

$$\sqrt{t +9} - \sqrt{t} = 1$$

Multiplying by $\sqrt{t +9} + \sqrt{t}$ you get

$$9=\sqrt{t +9} +\sqrt{t} $$

Now adding

$$\sqrt{t +9} + \sqrt{t} =9$$ $$\sqrt{t +9} - \sqrt{t} = 1$$

you get

$$\sqrt{t+9}=5 \Rightarrow t=25-9 $$