Solve: $r - 2 = \sqrt { 7 r - 6 }$
A) $\{ - 1 \}$
B) $\{ 10 \}$
C) no solution
D) $\{ - 10 , - 1 \}$

Question

Quizplus · Accepted Answer

To solve the equation $r - 2 = \sqrt { 7 r - 6 }$, we square both sides to eliminate the square root, resulting in $r^2 - 4r + 4 = 7r - 6$. Rearranging gives $r^2 - 11r + 10 = 0$, which factors to $(r - 1)(r - 10) = 0$. Thus, $r = 1$ or $r = 10$. However, substituting $r = 1$ back into the original equation gives a contradiction ($1 - 2 \neq \sqrt{7(1) - 6}$), so the only valid solution is $r = 10$.

Solve r−2=7r−6r - 2 = \sqrt { 7 r - 6 }r−2=7r−6​

Solve $r - 2 = \sqrt { 7 r - 6 }$