Amie and Joe are asked to pick values for the numbers $p$, $q$, and $r$ so that the following is true for all $a \, ext{in} \, ext{R} :$ $$p^a \times q^a \times r^a = q^{12}$$ (i) Amie picked three values that were all the same, so $p = q = r$. Write down the values of $p$, $q$, and $r$ that Amie picked. (ii) Joe picked three values that were all different. Write down possible values of $p$, $q$, and $r$ that Joe might have picked.

Junior Cycle Mathematics ALGEBRA - Expressions: Amie and Joe are asked to pick v

Amie and Joe are asked to pick values for the numbers $p$, $q$, and $r$ so that the following is true for all $a \, ext{in} \, ext{R} :$ $$p^a \times q^a \times r^a = q^{12}$$ (i) Amie picked three values that were all the same, so $p = q = r$ - Junior Cycle Mathematics - Question 7 - 2022

Question 7

$Amie-and-Joe-are-asked-to-pick-values-for-the-numbers-$p$,-$q$,-and-$r$-so-that-the-following-is-true-for-all-$a-\,--ext{in}-\,--ext{R}-:$---$$p^a-\times-q^a-\times-r^a-=-q^{12}$$--(i)-Amie-picked-three-values-that-were-all-the-same,-so-$p-=-q-=-r$-Junior Cycle Mathematics-Question 7-2022.png$

Amie and Joe are asked to pick values for the numbers $p$, $q$, and $r$ so that the following is true for all $a \, ext{in} \, ext{R} :$ $$p^a \times q^a \times ... show full transcript

Worked Solution & Example Answer:Amie and Joe are asked to pick values for the numbers $p$, $q$, and $r$ so that the following is true for all $a \, ext{in} \, ext{R} :$ $$p^a \times q^a \times r^a = q^{12}$$ (i) Amie picked three values that were all the same, so $p = q = r$ - Junior Cycle Mathematics - Question 7 - 2022

Step 1

Amie picked three values that were all the same, so $p = q = r$.

96%

114 rated

Answer

Since Amie chose all the same values for $p$ , $q$ , and $r$ , we can write:

p = q = r = 4\ ext{(this satisfies } p^a \times q^a \times r^a = r^{12}) \end{align*}$$

Step 2

Joe picked three values that were all different.

99%

104 rated

Answer

For Joe's case, we need three different values that add up to 12. One example could be:

p = 0, \ q = -1.5, \ r = 13.5\ ext{(these values are all different and sum to 12)}\ \end{align*}$$ Other combinations could also work, such as $p = 3$, $q = 4$, $r = 5$.

Amie and Joe are asked to pick values for the numbers $p$, $q$, and $r$ so that the following is true for all $a \, ext{in} \, ext{R} :$ $$p^a \times q^a \times r^a = q^{12}$$ (i) Amie picked three values that were all the same, so $p = q = r$ - Junior Cycle Mathematics - Question 7 - 2022

Amie picked three values that were all the same, so $p = q = r$.

Joe picked three values that were all different.

Join the Junior Cycle students using SimpleStudy...