Question

Error analysis: You are going to find the error(s) in the math work shown below. Explain any errors completely, then enter the correct solution including the correct steps. For both problems

Thank you
please answer​

Answer 1

See below ~

Explanation:

Analyzing Question 2 :

⇒
`\sqrt{(15)/(2) }`

⇒
`(√(15) )/(√(2) )` (Correct)

⇒
`(√(15) )/(√(2) ) * (√(2) )/(√(2) )` (Correct)

⇒
`(√(30) )/(√(2))` (Incorrect ×)

This step is incorrect because on multiplying the denominator it should be √4, equal to 2.

The correct step will be :

⇒
`(√(30) )/(2)` (Correct) (Final solution)

Analyzing Question 3 :

⇒
`x^(2) - 4 = 0`

⇒
`\sqrt{x^(2) -4} = 0` (Step is theoretically correct, but solution won't be possible here)

⇒
`x-2=0` (Incorrect ×)

This step is incorrect because the square root of x² - 4 cannot be taken. (x - 2) would be the value of the root of (x - 2)² = x² - 4x + 4.

Resolving by alternative method :

⇒
`x^(2) = 4` (Correct)

⇒
`\sqrt{x^(2) } = √(4)` (Correct)

⇒ x = ±2 (Correct) (Final solution)