Extraneous Solutions
Understand extraneous solutions in Grade 9 math — Squaring can create imposter answers that don't actually work. Part of Advanced Topics in Algebra for Grade 9.
Key Concepts
Property An answer from a derived equation that does not work in the original equation. Always check your work! Explanation Watch out for fakes! Squaring can create imposter answers that don't actually work. You must plug your final answer back into the original equation to check if it's a real solution or a tricky extraneous one. Examples Solve $\sqrt{x 2}=x 4$. Solutions are $x=3$ and $x=6$. Only $x=6$ works. Solve $\sqrt{x+7}= 3$. Squaring gives $x=2$, but $\sqrt{9} \neq 3$. No solution.
Common Questions
What is 'Extraneous Solutions' in Grade 9 math?
Squaring can create imposter answers that don't actually work. You must plug your final answer back into the original equation to check if it's a real solution or a tricky extraneous one.
How do you solve problems involving 'Extraneous Solutions'?
You must plug your final answer back into the original equation to check if it's a real solution or a tricky extraneous one. Squaring gives $x=2$, but $\sqrt{9} \neq -3$.
Why is 'Extraneous Solutions' an important Grade 9 math skill?
Remember, the negative sign in the exponent tells you to take the reciprocal (flip it!), not to change the sign of the base.. So, $5^{-2} = \frac{1}{5^2} = \frac{1}{25}$, which is a positive number!.