1. **State the problem:** We have four equations involving flower values: - Pink flower $p$ times pink flower $p$ equals 9: $p \times p = 9$. - $(p + o)^2 = 25$, where $o$ is orange flower. - $p + o - (p - o) = r$, where $r$ is red flower. - Find $p + r \times r - o$. 2. **Use the formulas and rules:** - From $p \times p = 9$, we get $p^2 = 9$. - From $(p + o)^2 = 25$, expand using $(a+b)^2 = a^2 + 2ab + b^2$. - Simplify the third equation. 3. **Solve for $p$:** $$p^2 = 9$$ Taking square root: $$p = \pm 3$$ 4. **Solve for $p + o$:** $$ (p + o)^2 = 25 $$ Taking square root: $$ p + o = \pm 5 $$ 5. **Simplify the third equation:** $$ p + o - (p - o) = r $$ Distribute the minus: $$ p + o - p + o = r $$ Simplify: $$ 2o = r $$ 6. **Express $r$ in terms of $o$:** $$ r = 2o $$ 7. **Find $p + r \times r - o$:** Substitute $r = 2o$: $$ p + (2o) \times (2o) - o = p + 4o^2 - o $$ 8. **Use $p + o = \pm 5$ to express $o$ in terms of $p$:** $$ o = \pm 5 - p $$ 9. **Try $p = 3$ and $p + o = 5$ (positive roots):** $$ o = 5 - 3 = 2 $$ $$ r = 2o = 4 $$ 10. **Calculate the expression:** $$ p + r \times r - o = 3 + 4 \times 4 - 2 = 3 + 16 - 2 = 17 $$ 11. **Check other root combinations:** - If $p = -3$ and $p + o = -5$, then $o = -5 - (-3) = -2$, $r = 2(-2) = -4$, expression: $$ -3 + (-4) \times (-4) - (-2) = -3 + 16 + 2 = 15 $$ - If $p = 3$ and $p + o = -5$, then $o = -5 - 3 = -8$, $r = 2(-8) = -16$, expression: $$ 3 + (-16) \times (-16) - (-8) = 3 + 256 + 8 = 267 $$ - If $p = -3$ and $p + o = 5$, then $o = 5 - (-3) = 8$, $r = 2(8) = 16$, expression: $$ -3 + 16 \times 16 - 8 = -3 + 256 - 8 = 245 $$ 12. **Choose the most reasonable positive solution:** $p = 3$, $o = 2$, $r = 4$, expression value = 17. **Final answer:** $$\boxed{17}$$