A student is asked to solve b2 + a2 = c2 for a and gives the following solution. Assume all variables represent positive Real Numbers.
b2 + a2 = c2
pb2 + a2 = pc2
b + a = c
a = c-b
Explain the mistake(s) made by the student and provide the correct solution.
p? do you mean √?
√(b^2+a^2) = √c^2
clearly the next step is flawed.
√(b^2+a^2) ≠ b+a
while √(b^2*a^2) = √b^2 * √a^2,
√(b^2+a^2) ≠ √b^2 + √a^2
I figure you can take it from there
a^2+b^2=c^2
a^2=c^2-b^2
a=square root of (c^2-b^2)
The mistake made by the student is in assuming that (pb^2 + a^2) can be simplified to b + a, and therefore equating it to c.
To understand why this assumption is incorrect, we need to look at the distributive property of multiplication. According to the distributive property, (pb^2 + a^2) does not simplify to b + a.
The correct way to solve the equation b^2 + a^2 = c^2 is as follows:
1. Start with the given equation b^2 + a^2 = c^2.
2. Rearrange the equation by subtracting b^2 from both sides: a^2 = c^2 - b^2.
3. Take the square root of both sides of the equation: √(a^2) = √(c^2 - b^2).
4. Simplify the equation: a = √(c^2 - b^2).
Therefore, the correct solution is a = √(c^2 - b^2).
It's important to remember that when solving equations, we need to follow the correct mathematical steps based on rules and properties, such as the distributive property and square root properties, to derive the accurate solution.