16Hit1600
Advanced MathVery hardDifference of squared radicals

Advanced Math practice question

For x > 0, the expression (√x + 1)² − (√x − 1)² is equivalent to k√x, where k is a constant. What is the value of k?

Answer: 4

(√x + 1)² = x + 2√x + 1 and (√x − 1)² = x − 2√x + 1; their difference is 4√x.

Common wrong answers

If you answered 0
0 assumes the squares are equal.
If you answered 1
1 comes from the constant terms, which cancel.
If you answered 2
2 counts only one of the two 2√x terms.

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