If the equation above is true, then what is the positive value of the expression `10 sqrtx-15` ?

Options

A. 20
B. 25
C. 30
D. 35

Answer

A

Explanation

The presence of 4,9 and 16- all perfect squares -is a big clue. Notye that `4x - 12 sqrtx +9` is an instance of the classic quadratic `(a-b)^(2) =a ^(2) -2ab+b ^(2).` Use this shortcut to factor the equation ans se where that leads you:
`4x -12 sqrtx +9 =16`
`(2 sqrtx -3) ^(2) =16`
`2 sqrtx -3 = pm4`
The question asks for `10 sqrtx-15,` which happens to be 5 times the quantity on the left side of the last equation above, so multiply the positive result, 4 by 5 to get 20. The correct answer is (A).