Luca solved an equation as shown, and verified that his solution was correct. Explain what Luca's error is and why his answer is not completely correct.

Question

Mathematics

Piglet

6 May, 12:23

Luca solved an equation as shown, and verified that his solution was correct. Explain what Luca's error is and why his answer is not completely correct.

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Answers (1)

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Siena Kramer · Answer 1

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Luca did not square the right side of the equation properly.

When the binomial with the radical term is squared, the result still has a radical.

After simplifying, both sides of the equation have to be squared again.

After simplifying, the resulting quadratic trinomial can be solved by factoring.

There are actually two solutions: x = 3 and x = 7.