Question

Please answer asap this person made a mistake what is the error and correct solution to this problem

Answer 1

Error : The expression ( 4 + x )² was expanded incorrectly.

Correct Solution : x = 6

Explanation:

The planning of the solution is correct, by Pythagorean Theorem you can say that PQ² + QO² = PO², and hence through substitution x² + 8² = ( 4 + x )². Let's look into the calculations.

PQ² + QO² = PO²,

x² + 8² = ( 4 + x )²,

x² + 8² = 16 + 8x + x²,

64 = 16 + 8x,

48 = 8x,

x = 48 / 8 = 6, x = 6

As you can see, the only error in the calculations was expanding the expression ( 4 + x )². ( 4 + x )² = 4² + 2
`*` 4
`*` x + x² = 4² + 8x + x² = 16 + 8x + x², not 16 + 4x + x².

Answer 2

6

Explanation:

Hello, please consider the following.

`(4+x)^2=4^2+2\cdot 4\cdot x+x^2=16+\boxed{8}x+x^2\\\\\text{ ... and not ...}\\\\16+\boxed{4}x+x^2`

So the correct equation becomes.

`x^2+64=16+8x+x^2\\\\8x=64-16=48\\\\\text{ we divide by 8 both sides of the equation.}\\\\x=(45)/(8)=6`

Hope this helps.

Do not hesitate if you need further explanation.

Thank you