Video: US-SAT04S3-Q15-937136307867

If π‘š > 0 and 𝑧 = 8 for the equation √(2π‘šΒ² + 14) βˆ’ 𝑧 = 0, what is the value of π‘š?

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Video Transcript

If π‘š is greater than zero and 𝑧 equals eight for the equation, the square root of two π‘š squared plus 14 minus 𝑧 equals zero, what is the value of π‘š?

We’re given in the question that the square root of two π‘š squared plus 14 minus 𝑧 is equal to zero? We’re also told that 𝑧 is equal to eight, so we can substitute in this value. This gives us the square root of two π‘š squared plus 14 minus eight is equal to zero. We now need to solve this equation to calculate the value of π‘š. Our first step is to add eight to both sides of the equation. On the left-hand side, negative eight plus eight is equal to zero. And on the right-hand side, zero plus eight equals eight. The inverse or opposite of square routing is squaring. This means that our next step is to square both sides of the equation. On the left-hand side, the square and square root cancel, leaving us with two π‘š squared plus 14. On the right-hand side, eight squared is equal to 64.

Next, we need to subtract 14 from both sides of this new equation. This gives us two π‘š squared is equal to 50. We can then divide both sides of this equation by two. Two π‘š squared divided by two is equal to π‘š squared. And 50 divided by two is equal to 25. Our final step is to square root both sides of this equation. The square root of π‘š squared is equal to π‘š. The square root of 25 has two answers, positive five and negative five, as positive Five squared is 25 and negative five squared is also 25. This suggests that we have two possible values for π‘š. However, we were told in the question that π‘š is greater than zero. This means that it must be positive. As π‘š is great than naught, the only value of π‘š that satisfies the equation is π‘š equals five.

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