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Algebra Level 2

Which solution to the equation x 2 = x x^2 = x contains an error?

A.

Original: x 2 = x Divide both sides by x: x = 1 \begin{aligned} \text{Original: }\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; x^2 &= x\\ \text{Divide both sides by x:}\;\;\;\;\; x &= 1 \end{aligned}

B.

Original: x 2 = x Subtract x from both sides: x 2 − x = 0 Factor: x ( x − 1 ) = 0 Use the Zero Product Property: x = 0 , x = 1 \begin{aligned} \text{Original: }\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; x^2 &= x\\ \text{Subtract x from both sides:}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x^2 - x &= 0\\ \text{Factor:}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; x(x-1) &= 0\\ \text{Use the Zero Product Property:}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; x =0&, x = 1 \end{aligned}

A Neither Both B

Damon Demas by Damon Demas

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1 solution

Kay Xspre
Mar 3, 2016

The first solution will be correct ONLY if x ≠ 0 x \neq 0 , however, since the second solution also noted that x = 0 x = 0 is a solution, division by zero (if x = 0 x = 0 ) will give invalid/undefined results.

6 Helpful 0 Interesting 0 Brilliant 0 Confused

The equation is a quadratic one but A converted it into linear giving only one of the solutions.

Kushagra Sahni - 5 years, 3 months ago

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