### Home > INT3 > Chapter 3 > Lesson 3.1.1 > Problem3-17

3-17.

Use the structure of each equation to rewrite it, as Graciela did in problem 3-6. Then solve one of the three equations completely, showing your work.

Substitute $U$ for the expressions in parentheses for each problem.

1. $\frac { 3 ( x ^ { 2 } - \frac { 4 } { 5 } ) } { 8 } + \frac { ( x ^ { 2 } - \frac { 4 } { 5 } ) } { 4 } = 2$

$U=x^2-\frac{4}{5}$

$\frac{3U}{8}+\frac{U}{4}=2$

$U=\frac{16}{5}$

$x=\pm2$

2. $( \frac { 1 } { n + 1 } ) ^ { 2 } + 6 ( \frac { 1 } { n + 1 } ) = 27$

Solve $U^2+6U=27$.

3. $6 ( \frac { x + 2 } { 6 } ) ^ { 2 } + 7 ( \frac { x + 2 } { 6 } ) - 3 = 0$

Follow the steps in part (a).