A pupil solves $x^2=6x$ by dividing both sides by $x$, and concludes that the only solution is \

Question

A pupil solves $x^2=6x$ by dividing both sides by $x$, and concludes that the only solution is $x=6$. Explain why this method may lose a solution.[1] Solve the equation and check both solutions in the original equation.[3]

Accepted Answer

(a) Dividing by $x$ excludes $x=0$. (b) $x=0$ or $x=6$; both satisfy the original equation.

Checking an algebraic method

Checking an algebraic method

Solution:

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