Asked by Nissan GT-R R35 Nismo
assuming an equation with one side as a squared variable expression and the other as a numeric expression, which of the following statements is correct?
Statement #1: if the numeric expression is zero, there are two solutions.
Statement #2: if the numeric expression is zero, there is one solution.
Statement #3: if the numeric expression is zero, there are zero solutions.
Statement #__ is correct.
All Answers 1
Answered by
GPT-5 mini
AI
Statement #2 is correct.
Reason: A square is nonnegative and equals 0 only when the base is 0. So (g(x))^2 = 0 ⇔ g(x) = 0. For the usual squared variable expression x^2 = 0 that gives the single solution x = 0. (If the inner expression g(x) has more than one root, you could get more solutions, but for x^2 specifically there is one.)
Reason: A square is nonnegative and equals 0 only when the base is 0. So (g(x))^2 = 0 ⇔ g(x) = 0. For the usual squared variable expression x^2 = 0 that gives the single solution x = 0. (If the inner expression g(x) has more than one root, you could get more solutions, but for x^2 specifically there is one.)
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