Question

Solve $9x^2=25$

• A. $-\frac{5}{3}$ or $\frac{5}{3}$
• B. $\frac{5}{3}$ or $\frac{5}{3}$
• C. $\frac{5}{3}$ or $-\frac{5}{3}$
• D. $\frac{3}{5}$ or $-\frac{3}{5}$

Answer 1

The correct option is A $-\frac{5}{3}$ or $\frac{5}{3}$

By transposition,
$9x^2-25=0$
or $(3x{)}^2-(5{)}^2=0$
or $(3x+5)(3x-5)=0$
i.e., $3x+5=0$ or $3x-5=0$
i.e., $x=-\frac{5}{3}$ or $\frac{5}{3}$
Hence, the solutions are $x=\frac{5}{3}$ and $-\frac{5}{3}$
This problem can also be solved as follows:
$9x^2-25=0$ or $x^2=\frac{25}{9}$ or $x=\pm \sqrt{\frac{25}{9}}=\pm \frac{5}{3}$